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Homological dimensions for endomorphism algebras of Gorenstein projective modules 戈伦斯坦投影模组内态代数的同调维数
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-08-28 DOI: 10.21136/cmj.2024.0199-23
Aiping Zhang, Xueping Lei
{"title":"Homological dimensions for endomorphism algebras of Gorenstein projective modules","authors":"Aiping Zhang, Xueping Lei","doi":"10.21136/cmj.2024.0199-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0199-23","url":null,"abstract":"<p>Let <i>A</i> be a CM-finite Artin algebra with a Gorenstein-Auslander generator <i>E, M</i> be a Gorenstein projective <i>A</i>-module and <i>B</i> = End<sub><i>A</i></sub><i>M</i>. We give an upper bound for the finitistic dimension of <i>B</i> in terms of homological data of <i>M</i>. Furthermore, if <i>A</i> is <i>n</i>-Gorenstein for 2 ⩽ <i>n</i> &lt; ∞, then we show the global dimension of <i>B</i> is less than or equal to <i>n</i> plus the <i>B</i>-projective dimension of Hom<sub><i>A</i></sub>(<i>M, E</i>). As an application, the global dimension of End<sub><i>A</i></sub><i>E</i> is less than or equal to <i>n</i>.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"18 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182226","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Non-weight modules over the super Schrödinger algebra 超薛定谔代数上的非重模块
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-08-28 DOI: 10.21136/cmj.2024.0030-23
Xinyue Wang, Liangyun Chen, Yao Ma
{"title":"Non-weight modules over the super Schrödinger algebra","authors":"Xinyue Wang, Liangyun Chen, Yao Ma","doi":"10.21136/cmj.2024.0030-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0030-23","url":null,"abstract":"<p>We construct a family of non-weight modules which are free <span>(U(frak{h}))</span>-modules of rank 2 over the <i>N</i> = 1 super Schrödinger algebra in (1+1)-dimensional spacetime. We determine the isomorphism classes of these modules. In particular, free <span>(U(frak{h}))</span>-modules of rank 2 over <span>(frak{osp}(1mid 2))</span> are also constructed and classified. Moreover, we obtain the sufficient and necessary conditions for such modules to be simple.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants $$cal{SO}_5$$ and $$cal{SO}_6$$ 与松博指数样图不变式 $$cal{SO}_5$$ 和 $$cal{SO}_6$$ 有关的极值树和分子树
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-08-27 DOI: 10.21136/cmj.2024.0221-24
Wei Gao
{"title":"Extremal trees and molecular trees with respect to the Sombor-index-like graph invariants $$cal{SO}_5$$ and $$cal{SO}_6$$","authors":"Wei Gao","doi":"10.21136/cmj.2024.0221-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0221-24","url":null,"abstract":"<p>I. Gutman (2022) constructed six new graph invariants based on geometric parameters, and named them Sombor-index-like graph invariants, denoted by <span>(cal{SO}_1, cal{SO}_2, dots, cal{SO}_6)</span>. Z. Tang, H. Deng (2022) and Z. Tang, Q. Li, H. Deng (2023) investigated the chemical applicability and extremal values of these Sombor-index-like graph invariants, and raised some open problems, see Z. Tang, Q. Li, H. Deng (2023). We consider the first open problem formulated at the end of Z. Tang, Q. Li, H. Deng (2023). We obtain the extremal values of the graph invariants <span>(cal{SO}_5)</span> and <span>(cal{SO}_6)</span> among all trees and molecular trees of order <i>n</i>, and characterize the trees and molecular trees that achieve the extremal values, respectively. Thus, the problem is completely solved.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"11 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Cotorsion pairs in comma categories 逗号类别中的同位语对
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-08-23 DOI: 10.21136/cmj.2024.0420-23
Yuan Yuan, Jian He, Dejun Wu
{"title":"Cotorsion pairs in comma categories","authors":"Yuan Yuan, Jian He, Dejun Wu","doi":"10.21136/cmj.2024.0420-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0420-23","url":null,"abstract":"<p>Let <span>(cal{A})</span> and <span>(cal{B})</span> be abelian categories with enough projective and injective objects, and <span>(T coloncal{A}rightarrowcal{B})</span> a left exact additive functor. Then one has a comma category (<span>(mathopen{cal{B} downarrow T})</span>). It is shown that if <span>(T coloncal{A}rightarrowcal{B})</span> is <span>(cal{X})</span>-exact, then is a (hereditary) cotorsion pair in <span>(cal{A})</span> and <img alt=\"\" src=\"//media.springernature.com/lw66/springer-static/image/art%3A10.21136%2FCMJ.2024.0420-23/MediaObjects/10587_2024_2023_Fig2_HTML.gif\" style=\"width:66px;max-width:none;\"/> is a (hereditary) cotorsion pair in <span>(cal{B})</span> if and only if <img alt=\"\" src=\"//media.springernature.com/lw128/springer-static/image/art%3A10.21136%2FCMJ.2024.0420-23/MediaObjects/10587_2024_2023_Fig3_HTML.gif\" style=\"width:128px;max-width:none;\"/> is a (hereditary) cotorsion pair in (<span>(mathopen{cal{B}downarrow T})</span>) and <span>(cal{X})</span> and <span>(cal{Y})</span> are closed under extensions. Furthermore, we characterize when special preenveloping classes in abelian categories <span>(cal{A})</span> and <span>(cal{B})</span> can induce special preenveloping classes in (<span>(mathopen{cal{B}downarrow T})</span>).</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"32 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182227","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Regularizing effect of the interplay between coefficients in some noncoercive integral functionals 某些非强制积分函数中系数间相互作用的正则效应
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-08-21 DOI: 10.21136/cmj.2024.0216-24
Aiping Zhang, Zesheng Feng, Hongya Gao
{"title":"Regularizing effect of the interplay between coefficients in some noncoercive integral functionals","authors":"Aiping Zhang, Zesheng Feng, Hongya Gao","doi":"10.21136/cmj.2024.0216-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0216-24","url":null,"abstract":"<p>We are interested in regularizing effect of the interplay between the coefficient of zero order term and the datum in some noncoercive integral functionals of the type</p><span>$$cal{J} (v)= int_Omega j(x,v,nabla v), {rm d}x +int_Omega a(x) vert vvert^{2} , {rm d} x -int_Omega fv , {rm d}x, quad vin W^{1,2}_{0}(Omega),$$</span><p>where Ω ⊂ ℝ<sup><i>N</i></sup>, <i>j</i> is a Carathéodory function such that <i>ξ</i> ↦ <i>j</i>(<i>x, s, ξ</i>) is convex, and there exist constants 0 ⩽ <i>τ</i> &lt; 1 and <i>M</i> &gt; 0 such that</p><span>$${vertxivert^{2}}{over{{(1+vert svert)^{tau}}}}leqslant j(x,s,xi)leqslant Mvertxivert^2$$</span><p>for almost all <i>x</i> ∈ Ω, all <i>s</i> ∈ ℝ and all <i>ξ</i> ∈ ℝ<sup><i>N</i></sup>. We show that, even if 0 &lt; <i>a</i>(<i>x</i>) and <i>f</i>(<i>x</i>) only belong to <i>L</i><sup>1</sup>(Ω), the interplay</p><span>$$vert f(x)vertleqslant2 Qa(x)$$</span><p>implies the existence of a minimizer <i>u</i> ∈ <i>W</i><span>\u0000<sup>1,2</sup><sub>0</sub>\u0000</span> (Ω) which belongs to <i>L</i><sup>∞</sup>(Ω).</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"148 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 linear maps leaving invariant the copositive/completely positive cones 关于使共正/完全正锥不变的线性映射
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-08-16 DOI: 10.21136/cmj.2024.0002-24
Sachindranath Jayaraman, Vatsalkumar N. Mer
{"title":"On linear maps leaving invariant the copositive/completely positive cones","authors":"Sachindranath Jayaraman, Vatsalkumar N. Mer","doi":"10.21136/cmj.2024.0002-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0002-24","url":null,"abstract":"<p>The objective of this manuscript is to investigate the structure of linear maps on the space of real symmetric matrices <span>(cal{S}^{n})</span> that leave invariant the closed convex cones of copositive and completely positive matrices (COP<sub><i>n</i></sub> and CP<sub><i>n</i></sub>). A description of an invertible linear map on <span>(cal{S}^{n})</span> such that <i>L</i>(CP<sub><i>n</i></sub>) ⊂ <i>CP</i><sub><i>n</i></sub> is obtained in terms of semipositive maps over the positive semidefinite cone <span>(cal{S}_{+}^{n})</span> and the cone of symmetric nonnegative matrices <span>(cal{N}_{+}^{n})</span> for <i>n</i> ⩽ 4, with specific calculations for <i>n</i> = 2. Preserver properties of the Lyapunov map <i>X</i> ↦ <i>AX</i> + <i>XA</i><sup><i>t</i></sup>, the generalized Lyapunov map <i>X</i> ↦ <i>AXB</i> + <i>B</i><sup><i>t</i></sup><i>XA</i><sup><i>t</i></sup>, and the structure of the dual of the cone <i>π</i>(CP<sub><i>n</i></sub>) (for <i>n</i> ⩽ 4) are brought out. We also highlight a different way to determine the structure of an invertible linear map on <span>(cal{S}^{2})</span> that leaves invariant the closed convex cone <span>(cal{S}_{+}^{2})</span>.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 ◦ operation and * operation of Cohen-Macaulay bipartite graphs 科恩-麦考莱双方形图的◦运算和＊运算
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-07-21 DOI: 10.21136/cmj.2024.0438-23
Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan
{"title":"The ◦ operation and * operation of Cohen-Macaulay bipartite graphs","authors":"Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan","doi":"10.21136/cmj.2024.0438-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0438-23","url":null,"abstract":"<p>Let <i>G</i> be a finite simple graph with the vertex set <i>V</i> and let <i>I</i><sub><i>G</i></sub> be its edge ideal in the polynomial ring <span>(S=mathbb{K}[V])</span>. We compute the depth and the Castelnuovo-Mumford regularity of <i>S</i>/<i>I</i><sub><i>G</i></sub> when <i>G</i> = <i>G</i><sub>1</sub> ◦ <i>G</i><sub>2</sub> or <i>G</i> = <i>G</i><sub>1</sub> * <i>G</i><sub>2</sub> is a graph obtained from Cohen-Macaulay bipartite graphs <i>G</i><sub>1</sub>, <i>G</i><sub>2</sub> by the ◦ operation or * operation, respectively.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"58 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces 准计量空间弱 Choquet 空间上的广义分数积分算子
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-07-18 DOI: 10.21136/cmj.2024.0133-24
Toshihide Futamura, Tetsu Shimomura
{"title":"Generalized fractional integral operators on weak Choquet spaces over quasi-metric measure spaces","authors":"Toshihide Futamura, Tetsu Shimomura","doi":"10.21136/cmj.2024.0133-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0133-24","url":null,"abstract":"<p>We prove the boundedness of the generalized fractional maximal operator <i>M</i><sub><i>α</i></sub> and the generalized fractional integral operator <i>I</i><sub><i>α</i></sub> on weak Choquet spaces with respect to Hausdorff content over quasi-metric measure spaces.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"61 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776991","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 covariety of perfect numerical semigroups with fixed Frobenius number 具有固定弗罗本尼斯数的完备数值半群的协方差
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-07-15 DOI: 10.21136/cmj.2024.0379-23
María Ángeles Moreno-Frías, José Carlos Rosales
{"title":"The covariety of perfect numerical semigroups with fixed Frobenius number","authors":"María Ángeles Moreno-Frías, José Carlos Rosales","doi":"10.21136/cmj.2024.0379-23","DOIUrl":"https://doi.org/10.21136/cmj.2024.0379-23","url":null,"abstract":"<p>Let <i>S</i> be a numerical semigroup. We say that <i>h</i> ∈ ℕ <i>S</i> is an isolated gap of <i>S</i> if {<i>h</i> − 1, <i>h</i> + 1} ⊆ <i>S</i>. A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by m(<i>S</i>) the multiplicity of a numerical semigroup <i>S</i>. A covariety is a nonempty family <span>(mathscr{C})</span> of numerical semigroups that fulfills the following conditions: there exists the minimum of <span>(mathscr{C})</span>, the intersection of two elements of <span>(mathscr{C})</span> is again an element of <span>(mathscr{C})</span>, and <span>(Sbackslash{{rm m}(S)}inmathscr{C})</span> for all <span>(Sinmathscr{C})</span> such that <span>(Sneqmin(mathscr{C}))</span>. We prove that the set <span>({mathscr{P}}(F)={Scolon S text{is} text{a} text{perfect} text{numerical} text{semigroup} text{with} text{Frobenius} text{number} F})</span> is a covariety. Also, we describe three algorithms which compute: the set <span>({mathscr{P}}(F))</span>, the maximal elements of <span>({mathscr{P}}(F))</span>, and the elements of <span>({mathscr{P}}(F))</span> with a given genus. A Parf-semigroup (or Psat-semigroup) is a perfect numerical semigroup that in addition is an Arf numerical semigroup (or saturated numerical semigroup), respectively. We prove that the sets Parf(<i>F</i>) = {<i>S</i>: <i>S</i> is a Parf-numerical semigroup with Frobenius number <i>F</i>} and Psat(<i>F</i>) = {<i>S</i>: <i>S</i> is a Psat-numerical semigroup with Frobenius number <i>F</i>} are covarieties. As a consequence we present some algorithms to compute Parf(<i>F</i>) and Psat(<i>F</i>).</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"45 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141929945","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Area differences under analytic maps and operators 解析图和算子下的面积差异
IF 0.5 4区 数学
Czechoslovak Mathematical Journal Pub Date : 2024-06-25 DOI: 10.21136/cmj.2024.0023-24
Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw
{"title":"Area differences under analytic maps and operators","authors":"Mehmet Çelik, Luke Duane-Tessier, Ashley Marcial Rodriguez, Daniel Rodriguez, Aden Shaw","doi":"10.21136/cmj.2024.0023-24","DOIUrl":"https://doi.org/10.21136/cmj.2024.0023-24","url":null,"abstract":"<p>Motivated by the relationship between the area of the image of the unit disk under a holomorphic mapping <i>h</i> and that of <i>zh</i>, we study various <i>L</i><sup>2</sup> norms for <i>T</i><sub><i>ϕ</i></sub>(<i>h</i>), where <i>T</i><sub><i>ϕ</i></sub> is the Toeplitz operator with symbol <i>ϕ</i>. In Theorem 2.1, given polynomials <i>p</i> and <i>q</i> we find a symbol <i>ϕ</i> such that <i>T</i><sub><i>ϕ</i></sub>(<i>p</i>) = <i>q</i>. We extend some of our results to the polydisc.</p>","PeriodicalId":50596,"journal":{"name":"Czechoslovak Mathematical Journal","volume":"13 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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