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On the Gowers trick for classical simple groups 关于经典简单群的高尔斯诀窍
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-28 DOI: 10.1016/j.jpaa.2024.107833
Francesco Fumagalli , Attila Maróti
{"title":"On the Gowers trick for classical simple groups","authors":"Francesco Fumagalli ,&nbsp;Attila Maróti","doi":"10.1016/j.jpaa.2024.107833","DOIUrl":"10.1016/j.jpaa.2024.107833","url":null,"abstract":"<div><div>If <em>A</em>, <em>B</em>, <em>C</em> are subsets in a finite simple group of Lie type <em>G</em> at least two of which are normal with <span><math><mo>|</mo><mi>A</mi><mo>|</mo><mo>|</mo><mi>B</mi><mo>|</mo><mo>|</mo><mi>C</mi><mo>|</mo></math></span> relatively large, then we establish a stronger conclusion than <span><math><mi>A</mi><mi>B</mi><mi>C</mi><mo>=</mo><mi>G</mi></math></span>. This is related to a theorem of Gowers and is a generalization of a theorem of Larsen, Shalev, Tiep and the second author and Pyber.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Flat relative Mittag-Leffler modules and Zariski locality 扁平相对米塔格-列夫勒模块和扎里斯基位置
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-28 DOI: 10.1016/j.jpaa.2024.107834
Asmae Ben Yassine, Jan Trlifaj
{"title":"Flat relative Mittag-Leffler modules and Zariski locality","authors":"Asmae Ben Yassine,&nbsp;Jan Trlifaj","doi":"10.1016/j.jpaa.2024.107834","DOIUrl":"10.1016/j.jpaa.2024.107834","url":null,"abstract":"<div><div>The ascent and descent of the Mittag-Leffler property were instrumental in proving Zariski locality of the notion of an (infinite dimensional) vector bundle by Raynaud and Gruson in <span><span>[26]</span></span>. More recently, relative Mittag-Leffler modules were employed in the theory of (infinitely generated) tilting modules and the associated quasi-coherent sheaves, <span><span>[2]</span></span>, <span><span>[22]</span></span>. Here, we study the ascent and descent along flat and faithfully flat homomorphisms for relative versions of the Mittag-Leffler property. In particular, we prove the Zariski locality of the notion of a locally f-projective quasi-coherent sheaf for all schemes, and for each <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, of the notion of an <em>n</em>-Drinfeld vector bundle for all locally noetherian schemes.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Almost Gorenstein simplicial semigroup rings 几乎戈伦斯坦简单半群环
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-26 DOI: 10.1016/j.jpaa.2024.107835
Kazufumi Eto , Naoyuki Matsuoka , Takahiro Numata , Kei-ichi Watanabe
{"title":"Almost Gorenstein simplicial semigroup rings","authors":"Kazufumi Eto ,&nbsp;Naoyuki Matsuoka ,&nbsp;Takahiro Numata ,&nbsp;Kei-ichi Watanabe","doi":"10.1016/j.jpaa.2024.107835","DOIUrl":"10.1016/j.jpaa.2024.107835","url":null,"abstract":"<div><div>We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion, we determine 2-dimensional normal semigroup rings which have “Ulrich elements” defined in <span><span>[8]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The centralizer of a locally nilpotent R-derivation of the polynomial R-algebra in two variables 二变量多项式 R 代数的局部零势 R 派生的中心子
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107828
M'hammed El Kahoui, Najoua Essamaoui, Mustapha Ouali
{"title":"The centralizer of a locally nilpotent R-derivation of the polynomial R-algebra in two variables","authors":"M'hammed El Kahoui,&nbsp;Najoua Essamaoui,&nbsp;Mustapha Ouali","doi":"10.1016/j.jpaa.2024.107828","DOIUrl":"10.1016/j.jpaa.2024.107828","url":null,"abstract":"<div><div>Let <em>R</em> be an integral domain containing <span><math><mi>Q</mi></math></span> and <em>ξ</em> be an irreducible nontrivial locally nilpotent <em>R</em>-derivation of the polynomial <em>R</em>-algebra <em>A</em> in two variables. In this paper we investigate the group <span><math><msub><mrow><mi>Aut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math></span> of <em>R</em>-automorphisms of <em>A</em> which commute with <em>ξ</em>. In the case <em>R</em> is a unique factorization domain and the plinth ideal of <em>ξ</em> is principal we give a complete description of the subgroup <span><math><msub><mrow><mi>SAut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math></span> of <span><math><msub><mrow><mi>Aut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math></span> consisting of Jacobian one automorphisms. If moreover <em>R</em> contains a field <em>K</em> such that the group of units of <em>R</em> is <span><math><msup><mrow><mi>K</mi></mrow><mrow><mo>⋆</mo></mrow></msup></math></span> we prove that <span><math><msub><mrow><mi>Aut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo><mo>=</mo><msub><mrow><mi>SAut</mi></mrow><mrow><mi>R</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>,</mo><mi>ξ</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characterization of affine Gm-surfaces of hyperbolic type 双曲型仿射 Gm 曲面的特征
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107829
Andriy Regeta
{"title":"Characterization of affine Gm-surfaces of hyperbolic type","authors":"Andriy Regeta","doi":"10.1016/j.jpaa.2024.107829","DOIUrl":"10.1016/j.jpaa.2024.107829","url":null,"abstract":"<div><div>In this note we extend the result from <span><span>[14]</span></span> and prove that if <em>S</em> is an affine non-toric <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>-surface of hyperbolic type that admits a <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>a</mi></mrow></msub></math></span>-action and <em>X</em> is an affine irreducible variety such that <span><math><mi>Aut</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span> is isomorphic to <span><math><mi>Aut</mi><mo>(</mo><mi>S</mi><mo>)</mo></math></span> as an abstract group, then <em>X</em> is a <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>-surface of hyperbolic type. Further, we show that a smooth Danielewski surface <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mo>{</mo><mi>x</mi><mi>y</mi><mo>=</mo><mi>p</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>}</mo><mo>⊂</mo><msup><mrow><mi>A</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, where <em>p</em> has no multiple roots, is determined by its automorphism group seen as an ind-group in the category of affine irreducible varieties.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Representations of quantum lattice vertex algebras 量子格顶点代数的表示
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107832
Fei Kong
{"title":"Representations of quantum lattice vertex algebras","authors":"Fei Kong","doi":"10.1016/j.jpaa.2024.107832","DOIUrl":"10.1016/j.jpaa.2024.107832","url":null,"abstract":"<div><div>Let <em>Q</em> be a non-degenerate even lattice, let <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow></msub></math></span> be the lattice vertex algebra associated to <em>Q</em>, and let <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span> be a quantum lattice vertex algebra (<span><span>[10]</span></span>). In this paper, we prove that every <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span>-module is completely reducible, and the set of simple <span><math><msubsup><mrow><mi>V</mi></mrow><mrow><mi>Q</mi></mrow><mrow><mi>η</mi></mrow></msubsup></math></span>-modules are in one-to-one correspondence with the set of cosets of <em>Q</em> in its dual lattice.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Characteristic modules and Gorenstein (co-)homological dimension of groups 特征模块和群的戈伦斯坦（共）同维度
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI: 10.1016/j.jpaa.2024.107830
Ioannis Emmanouil, Olympia Talelli
{"title":"Characteristic modules and Gorenstein (co-)homological dimension of groups","authors":"Ioannis Emmanouil,&nbsp;Olympia Talelli","doi":"10.1016/j.jpaa.2024.107830","DOIUrl":"10.1016/j.jpaa.2024.107830","url":null,"abstract":"<div><div>In this paper, we examine the Gorenstein dimension of modules over the group algebra <em>kG</em> of a group <em>G</em> with coefficients in a commutative ring <em>k</em>. As a Gorenstein analogue of the classical case, we bound this dimension in terms of the Gorenstein dimension of the underlying <em>k</em>-module and the Gorenstein dimension of <em>G</em> over <em>k</em>. Our method is based on the notion of a characteristic module for <em>G</em>, introduced by the second author, and uses the stability properties of the Gorenstein categories. We also examine the class of hierarchically decomposable groups defined by Kropholler and use the module of bounded <span><math><mi>Z</mi></math></span>-valued functions on such a group <em>G</em> to characterize the Gorenstein flat <span><math><mi>Z</mi><mi>G</mi></math></span>-modules, in terms of flat modules, and the Gorenstein injective <span><math><mi>Z</mi><mi>G</mi></math></span>-modules, in terms of injective modules (by complete analogy with the characterization of Gorenstein projective <span><math><mi>Z</mi><mi>G</mi></math></span>-modules, in terms of projective modules, obtained by Dembegioti and the second author). It follows that, for a group <em>G</em> in Kropholler's class, (a) any Gorenstein projective <span><math><mi>Z</mi><mi>G</mi></math></span>-module is Gorenstein flat and (b) a <span><math><mi>Z</mi><mi>G</mi></math></span>-module is Gorenstein flat if its Pontryagin dual module is Gorenstein injective.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A binary tree of complete intersections with the strong Lefschetz property 具有强列夫谢茨特性的二叉完全相交树
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107825
Tadahito Harima , Satoru Isogawa , Junzo Watanabe
{"title":"A binary tree of complete intersections with the strong Lefschetz property","authors":"Tadahito Harima ,&nbsp;Satoru Isogawa ,&nbsp;Junzo Watanabe","doi":"10.1016/j.jpaa.2024.107825","DOIUrl":"10.1016/j.jpaa.2024.107825","url":null,"abstract":"<div><div>In this paper we give a new family of complete intersections which have the strong Lefschetz property. The family consists of Artinian algebras defined by ideals generated by power sum symmetric polynomials of consecutive degrees and of certain ideals naturally derived from them. This family has a structure of a binary tree and this observation is a key to prove that all members in it have the strong Lefschetz property.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142533598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Periodic derived Hall algebras of hereditary abelian categories 遗传无性类的周期派生霍尔代数
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107824
Haicheng Zhang
{"title":"Periodic derived Hall algebras of hereditary abelian categories","authors":"Haicheng Zhang","doi":"10.1016/j.jpaa.2024.107824","DOIUrl":"10.1016/j.jpaa.2024.107824","url":null,"abstract":"<div><div>Let <em>m</em> be a positive integer and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span> be the <em>m</em>-periodic derived category of a finitary hereditary abelian category <span><math><mi>A</mi></math></span>. Applying the derived Hall numbers of the bounded derived category <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>b</mi></mrow></msup><mo>(</mo><mi>A</mi><mo>)</mo></math></span>, we define an <em>m</em>-periodic extended derived Hall algebra for <span><math><msub><mrow><mi>D</mi></mrow><mrow><mi>m</mi></mrow></msub><mo>(</mo><mi>A</mi><mo>)</mo></math></span>, and use it to give a global, unified and explicit characterization for the algebra structure of Bridgeland's Hall algebra of periodic complexes. Moreover, we also provide an explicit characterization for the odd periodic derived Hall algebra of <span><math><mi>A</mi></math></span> defined by Xu-Chen <span><span>[24]</span></span>.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142444585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Krull-Gabriel dimension of cluster repetitive categories and cluster-tilted algebras 关于簇重复范畴和簇倾斜代数的克鲁尔-加布里埃尔维度
IF 0.7 2区 数学
Journal of Pure and Applied Algebra Pub Date : 2024-10-16 DOI: 10.1016/j.jpaa.2024.107823
Alicja Jaworska-Pastuszak, Grzegorz Pastuszak, Grzegorz Bobiński
{"title":"On Krull-Gabriel dimension of cluster repetitive categories and cluster-tilted algebras","authors":"Alicja Jaworska-Pastuszak,&nbsp;Grzegorz Pastuszak,&nbsp;Grzegorz Bobiński","doi":"10.1016/j.jpaa.2024.107823","DOIUrl":"10.1016/j.jpaa.2024.107823","url":null,"abstract":"<div><div>Assume that <em>K</em> is an algebraically closed field and denote by <span><math><mi>KG</mi><mo>(</mo><mi>R</mi><mo>)</mo></math></span> the Krull-Gabriel dimension of <em>R</em>, where <em>R</em> is a locally bounded <em>K</em>-category (or a bound quiver <em>K</em>-algebra). Assume that <em>C</em> is a tilted <em>K</em>-algebra and <span><math><mover><mrow><mi>C</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>,</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˇ</mo></mrow></mover><mo>,</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover></math></span> are the associated repetitive category, cluster repetitive category and cluster-tilted algebra, respectively. Our first result states that <span><math><mi>KG</mi><mo>(</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo><mo>=</mo><mi>KG</mi><mo>(</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˇ</mo></mrow></mover><mo>)</mo><mo>≤</mo><mi>KG</mi><mo>(</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo></math></span>. Since the Krull-Gabriel dimensions of tame locally support-finite repetitive categories are known, we further conclude that <span><math><mi>KG</mi><mo>(</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>˜</mo></mrow></mover><mo>)</mo><mo>=</mo><mi>KG</mi><mo>(</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˇ</mo></mrow></mover><mo>)</mo><mo>=</mo><mi>KG</mi><mo>(</mo><mover><mrow><mi>C</mi></mrow><mrow><mo>ˆ</mo></mrow></mover><mo>)</mo><mo>∈</mo><mo>{</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>∞</mo><mo>}</mo></math></span>. Finally, in the Appendix Grzegorz Bobiński presents a different way of determining the Krull-Gabriel dimension of the cluster-tilted algebras, by applying results of Geigle.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142444584","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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