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Rationality of weighted hypersurfaces of special degree 特级加权超曲面的合理性
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.032
Michael Chitayat
{"title":"Rationality of weighted hypersurfaces of special degree","authors":"Michael Chitayat","doi":"10.1016/j.jalgebra.2024.10.032","DOIUrl":"10.1016/j.jalgebra.2024.10.032","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi><mo>⊂</mo><mi>P</mi><mo>(</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span> be a quasismooth well-formed weighted projective hypersurface and let <span><math><mi>L</mi><mo>=</mo><mi>lcm</mi><mo>(</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>w</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>)</mo></math></span>. We characterize when <em>X</em> is rational under the assumption that <em>L</em> divides <span><math><mi>deg</mi><mo>⁡</mo><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. Furthermore, we give a new family of normal rational weighted projective hypersurfaces with ample canonical divisor, valid in all dimensions, adding to the list of examples discovered by Kollár. Finally, we determine precisely which affine Pham-Brieskorn threefolds are rational, answering a question of Rajendra V. Gurjar.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 7-29"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705017","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
Higher torsion-free Auslander-Reiten sequences and the dominant dimension of algebras 更高的无扭 Auslander-Reiten 序列和代数的主维
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.11.004
Tiago Cruz , René Marczinzik
{"title":"Higher torsion-free Auslander-Reiten sequences and the dominant dimension of algebras","authors":"Tiago Cruz ,&nbsp;René Marczinzik","doi":"10.1016/j.jalgebra.2024.11.004","DOIUrl":"10.1016/j.jalgebra.2024.11.004","url":null,"abstract":"<div><div>We generalise a theorem of Tachikawa about reflexive Auslander-Reiten sequences. We apply this to give a new characterisation of the dominant dimension of gendo-symmetric algebras. We also generalise a formula due to Reiten about the dominant dimension of an algebra <em>A</em> and grades of torsion <em>A</em>-modules.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 282-297"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720428","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
On the number of quaternion and dihedral braces and Hopf–Galois structures 论四元数、二面括号和霍普夫-伽罗瓦结构
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.11.011
Nigel P. Byott , Fabio Ferri
{"title":"On the number of quaternion and dihedral braces and Hopf–Galois structures","authors":"Nigel P. Byott ,&nbsp;Fabio Ferri","doi":"10.1016/j.jalgebra.2024.11.011","DOIUrl":"10.1016/j.jalgebra.2024.11.011","url":null,"abstract":"<div><div>We prove a conjecture of Guarnieri and Vendramin on the number of braces of a given order whose multiplicative group is a generalised quaternion group. At the same time, we give a similar result where the multiplicative group is dihedral. We also enumerate Hopf-Galois structures of abelian type on Galois extensions with generalised quaternion or dihedral Galois group.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 72-102"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705021","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
Non-associative Frobenius algebras of type E61 with trivial Tits algebras E61 型非共轭弗罗贝尼斯代数与微不足道的 Tits 代数
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.035
Jari Desmet
{"title":"Non-associative Frobenius algebras of type E61 with trivial Tits algebras","authors":"Jari Desmet","doi":"10.1016/j.jalgebra.2024.10.035","DOIUrl":"10.1016/j.jalgebra.2024.10.035","url":null,"abstract":"<div><div>Very recently, Maurice Chayet and Skip Garibaldi have introduced a class of commutative non-associative algebras, for each simple linear algebraic group over an arbitrary field (with some minor restriction on the characteristic). In a previous paper, we gave an explicit description of these algebras for groups of type <span><math><msub><mrow><mi>G</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>F</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> in terms of the octonion algebras and the Albert algebras, respectively. In this paper, we attempt a similar approach for type <span><math><msub><mrow><mi>E</mi></mrow><mrow><mn>6</mn></mrow></msub></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 205-228"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142704945","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
The diagonal set of the self-product of an algebraic curve 代数曲线自积的对角集
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.050
Masayoshi Miyanishi
{"title":"The diagonal set of the self-product of an algebraic curve","authors":"Masayoshi Miyanishi","doi":"10.1016/j.jalgebra.2024.10.050","DOIUrl":"10.1016/j.jalgebra.2024.10.050","url":null,"abstract":"<div><div>Let <em>C</em> be a smooth projective curve of genus <em>g</em> defined over an algebraically closed field of characteristic <span><math><mi>p</mi><mo>≠</mo><mn>2</mn></math></span> and let Δ be the diagonal of <span><math><mi>C</mi><mo>×</mo><mi>C</mi></math></span>. We observe the complement <span><math><mi>X</mi><mo>:</mo><mo>=</mo><mo>(</mo><mi>C</mi><mo>×</mo><mi>C</mi><mo>)</mo><mo>∖</mo><mi>Δ</mi></math></span>. If <span><math><mi>g</mi><mo>=</mo><mn>0</mn></math></span>, <em>X</em> is an affine hypersurface <span><math><mi>x</mi><mi>y</mi><mo>=</mo><msup><mrow><mi>z</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mn>1</mn></math></span> in <span><math><msup><mrow><mi>A</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> which is the simplest example of Danielewski surfaces. If <span><math><mi>g</mi><mo>=</mo><mn>1</mn></math></span> then Δ is a fiber of an elliptic fibration over <em>C</em> so that <span><math><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mn>0</mn></math></span> and <span><math><mover><mrow><mi>κ</mi></mrow><mo>‾</mo></mover><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mn>1</mn></math></span>, and if <span><math><mi>g</mi><mo>&gt;</mo><mn>1</mn></math></span>, <span><math><mo>(</mo><msup><mrow><mi>Δ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo><mo>=</mo><mn>2</mn><mo>−</mo><mn>2</mn><mi>g</mi></math></span> and Δ is contractible. In the case <em>C</em> has genus <span><math><mi>g</mi><mo>&gt;</mo><mn>1</mn></math></span>, <em>X</em> is embedded bijectively into the Jacobian variety if <em>C</em> is non-hyperelliptic, though <em>X</em> is generically a double covering of a surface in the Jacobian variety if <em>C</em> is hyperelliptic. Some observations will be made in the case <em>k</em> has characteristic 2.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 39-47"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705020","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 the regularity of squarefree part of symbolic powers of edge ideals 论边理想符号幂的无平方部分的规则性
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.046
S.A. Seyed Fakhari
{"title":"On the regularity of squarefree part of symbolic powers of edge ideals","authors":"S.A. Seyed Fakhari","doi":"10.1016/j.jalgebra.2024.10.046","DOIUrl":"10.1016/j.jalgebra.2024.10.046","url":null,"abstract":"<div><div>Assume that <em>G</em> is a graph with edge ideal <span><math><mi>I</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span>. For every integer <span><math><mi>s</mi><mo>≥</mo><mn>1</mn></math></span>, we denote the squarefree part of the <em>s</em>-th symbolic power of <span><math><mi>I</mi><mo>(</mo><mi>G</mi><mo>)</mo></math></span> by <span><math><mi>I</mi><msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>{</mo><mi>s</mi><mo>}</mo></mrow></msup></math></span>. We determine an upper bound for the regularity of <span><math><mi>I</mi><msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>{</mo><mi>s</mi><mo>}</mo></mrow></msup></math></span> when <em>G</em> is a chordal graph. If <em>G</em> is a Cameron-Walker graph, we compute <span><math><mrow><mi>reg</mi></mrow><mo>(</mo><mi>I</mi><msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>{</mo><mi>s</mi><mo>}</mo></mrow></msup><mo>)</mo></math></span> in terms of the induced matching number of <em>G</em>. Moreover, for any graph <em>G</em>, we provide sharp upper bounds for <span><math><mrow><mi>reg</mi></mrow><mo>(</mo><mi>I</mi><msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>{</mo><mn>2</mn><mo>}</mo></mrow></msup><mo>)</mo></math></span> and <span><math><mrow><mi>reg</mi></mrow><mo>(</mo><mi>I</mi><msup><mrow><mo>(</mo><mi>G</mi><mo>)</mo></mrow><mrow><mo>{</mo><mn>3</mn><mo>}</mo></mrow></msup><mo>)</mo></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 103-130"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705022","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
Étale degree map and 0-cycles 埃塔尔度图和 0 循环
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.036
Iván Rosas-Soto
{"title":"Étale degree map and 0-cycles","authors":"Iván Rosas-Soto","doi":"10.1016/j.jalgebra.2024.10.036","DOIUrl":"10.1016/j.jalgebra.2024.10.036","url":null,"abstract":"<div><div>Using the triangulated category of étale motives over a field <em>k</em>, for a smooth projective variety <em>X</em> over <em>k</em>, we define the group <span><math><msubsup><mrow><mtext>CH</mtext></mrow><mrow><mn>0</mn></mrow><mrow><mtext>ét</mtext></mrow></msubsup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> as an étale analogue of 0-cycles. We study the properties of <span><math><msubsup><mrow><mtext>CH</mtext></mrow><mrow><mn>0</mn></mrow><mrow><mtext>ét</mtext></mrow></msubsup><mo>(</mo><mi>X</mi><mo>)</mo></math></span> and give a description of the birational invariance of such a group. We define and present the étale degree map using Gysin morphisms in étale motivic cohomology and the étale index as an analogue to the classical case. We give examples of smooth projective varieties over a field <em>k</em> without zero cycles of degree one but with étale zero cycles of degree one, but this property is not always true as we give examples where the étale degree map is not surjective.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 384-414"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720430","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
Classification of right nilpotent Fp-braces of cardinality p5 基数p5的右幂零fp -括号的分类
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.11.009
Snehashis Mukherjee
{"title":"Classification of right nilpotent Fp-braces of cardinality p5","authors":"Snehashis Mukherjee","doi":"10.1016/j.jalgebra.2024.11.009","DOIUrl":"10.1016/j.jalgebra.2024.11.009","url":null,"abstract":"<div><div>In this article the right nilpotent <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-braces of cardinality <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span> has been classified. We use the connection between nilpotent <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-braces of cardinality <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span> and nilpotent pre-Lie algebras of the same order, building on the known relationship between pre-Lie algebras and braces. Leveraging insights from the classification of nilpotent pre-Lie algebras over <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>, we aim to provide a comprehensive classification of right nilpotent <span><math><msub><mrow><mi>F</mi></mrow><mrow><mi>p</mi></mrow></msub></math></span>-braces of cardinality <span><math><msup><mrow><mi>p</mi></mrow><mrow><mn>5</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 503-537"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745177","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
The Eaton–Moretó Conjecture and p-solvable groups 埃顿-莫雷托猜想和可解 p 群
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.038
Gabriel Navarro
{"title":"The Eaton–Moretó Conjecture and p-solvable groups","authors":"Gabriel Navarro","doi":"10.1016/j.jalgebra.2024.10.038","DOIUrl":"10.1016/j.jalgebra.2024.10.038","url":null,"abstract":"<div><div>We prove that the Eaton–Moretó Conjecture is true for the principal blocks of the <em>p</em>-solvable groups.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 1-6"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142705019","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
Regular decompositions of finite root systems and simple Lie algebras 有限根系和简单李代数的正则分解
IF 0.8 2区 数学
Journal of Algebra Pub Date : 2024-11-19 DOI: 10.1016/j.jalgebra.2024.10.037
Stepan Maximov
{"title":"Regular decompositions of finite root systems and simple Lie algebras","authors":"Stepan Maximov","doi":"10.1016/j.jalgebra.2024.10.037","DOIUrl":"10.1016/j.jalgebra.2024.10.037","url":null,"abstract":"<div><div>Let <span><math><mi>g</mi></math></span> be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic 0. In this paper we classify all regular decompositions of <span><math><mi>g</mi></math></span> and its irreducible root system Δ.</div><div>A regular decomposition is a decomposition <span><math><mi>g</mi><mo>=</mo><msub><mrow><mi>g</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊕</mo><mo>…</mo><mo>⊕</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, where each <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊕</mo><msub><mrow><mi>g</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> are regular subalgebras. Such a decomposition induces a partition of the corresponding root system, i.e. <span><math><mi>Δ</mi><mo>=</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>⊔</mo><mo>…</mo><mo>⊔</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>m</mi></mrow></msub></math></span>, such that all <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>Δ</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>⊔</mo><msub><mrow><mi>Δ</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> are closed.</div><div>Partitions of Δ with <span><math><mi>m</mi><mo>=</mo><mn>2</mn></math></span> were known before. In this paper we prove that the case <span><math><mi>m</mi><mo>⩾</mo><mn>3</mn></math></span> is possible only for systems of type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> and describe all such partitions in terms of <em>m</em>-partitions of <span><math><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span>. These results are then extended to a classification of regular decompositions of <span><math><mi>g</mi></math></span>.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"665 ","pages":"Pages 415-440"},"PeriodicalIF":0.8,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142720431","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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