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International Electronic Journal of Algebra最新文献

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Computational methods for $t$-spread monomial ideals t$ 展开单项式理想的计算方法
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-11-16 DOI: 10.24330/ieja.1402973
Luca Amata
{"title":"Computational methods for $t$-spread monomial ideals","authors":"Luca Amata","doi":"10.24330/ieja.1402973","DOIUrl":"https://doi.org/10.24330/ieja.1402973","url":null,"abstract":"Let $K$ be a field and $S=K[x_1,ldots,x_n]$ a standard polynomial ring over $K$. In this paper, we give new combinatorial algorithms to compute the smallest $t$-spread lexicographic set and the smallest $t$-spread strongly stable set containing a given set of $t$-spread monomials of $S$. Some technical tools allowing to compute the cardinality of $t$-spread strongly stable sets avoiding their construction are also presented. Such functions are also implemented in a emph{Macaulay2} package, texttt{TSpreadIdeals}, to ease the computation of well-known results about algebraic invariants for $t$-spread ideals.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"24 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139269650","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Normality of Rees algebras of generalized mixed product ideals 广义混合乘积理想的里斯代数的规范性
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-10-30 DOI: 10.24330/ieja.1402961
M. La Barbiera, R. Moghimipor
{"title":"Normality of Rees algebras of generalized mixed product ideals","authors":"M. La Barbiera, R. Moghimipor","doi":"10.24330/ieja.1402961","DOIUrl":"https://doi.org/10.24330/ieja.1402961","url":null,"abstract":"Let $K$ be a field and $K[x_1,x_{2}]$ the polynomial ring in two variables over $K$ with each $x_i$ of degree $1$. Let $L$ be the generalized mixed product ideal induced by a monomial ideal $Isubset K[x_1,x_2]$, where the ideals substituting the monomials in $I$ are squarefree Veronese ideals. In this paper, we study the integral closure of $L$, and the normality of $mathcal{R}(L)$, the Rees algebra of $L$. Furthermore, we give a geometric description of the integral closure of $mathcal{R}(L)$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"54 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139311249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strongly J-n-Coherent rings 强 J-n 相干环
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-10-28 DOI: 10.24330/ieja.1411161
Zhanmin Zhu
{"title":"Strongly J-n-Coherent rings","authors":"Zhanmin Zhu","doi":"10.24330/ieja.1411161","DOIUrl":"https://doi.org/10.24330/ieja.1411161","url":null,"abstract":"Let $R$ be a ring and $n$ a fixed positive integer. A right $R$-module $M$ is called strongly $J$-$n$-injective if every $R$-homomorphism from an $n$-generated small submodule of a free right $R$-module $F$ to $M$ extends to a homomorphism of $F$ to $M$; a right $R$-module $V$ is said to be strongly $J$-$n$-flat, if for every $n$-generated small submodule $T$ of a free left $R$-module $F$, the canonical map $Votimes Trightarrow Votimes F$ is monic; a ring $R$ is called left strongly $J$-$n$-coherent if every $n$-generated small submodule of a free left $R$-module is finitely presented; a ring $R$ is said to be left $J$-$n$-semihereditary if every $n$-generated small left ideal of $R$ is projective. We study strongly $J$-$n$-injective modules, strongly $J$-$n$-flat modules and left strongly $J$-$n$-coherent rings. Using the concepts of strongly $J$-$n$-injectivity and strongly $J$-$n$-flatness of modules, we also present some characterizations of strongly $J$-$n$-coherent rings and $J$-$n$-semihereditary rings.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"226 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139312309","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strongly Graded Modules and Positively Graded Modules which are Unique Factorization Modules 作为唯一因式分解模块的强分级模块和正分级模块
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-10-18 DOI: 10.24330/ieja.1404435
Iwan Ernanto, Indah E. Wijayanti, Akira Ueda
{"title":"Strongly Graded Modules and Positively Graded Modules which are Unique Factorization Modules","authors":"Iwan Ernanto, Indah E. Wijayanti, Akira Ueda","doi":"10.24330/ieja.1404435","DOIUrl":"https://doi.org/10.24330/ieja.1404435","url":null,"abstract":"Let $M=oplus_{nin mathbb{Z}}M_{n}$ be a strongly graded module over strongly graded ring $D=oplus_{nin mathbb{Z}} D_{n}$. In this paper, we prove that if $M_{0}$ is a unique factorization module (UFM for short) over $D_{0}$ and $D$ is a unique factorization domain (UFD for short), then $M$ is a UFM over $D$. Furthermore, if $D_{0}$ is a Noetherian domain, we give a necessary and sufficient condition for a positively graded module $L=oplus_{nin mathbb{Z}_{0}}M_{n}$ to be a UFM over positively graded domain $R=oplus_{nin mathbb{Z}_{0}}D_{n}$.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"27 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139317380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The structure of certain unique classes of seminearrings 某些独特的半圆类的结构
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-10-18 DOI: 10.24330/ieja.1402798
G. Mani̇kandan, Perumal Ramachandran, P. Madhusoodhanan
{"title":"The structure of certain unique classes of seminearrings","authors":"G. Mani̇kandan, Perumal Ramachandran, P. Madhusoodhanan","doi":"10.24330/ieja.1402798","DOIUrl":"https://doi.org/10.24330/ieja.1402798","url":null,"abstract":"In this paper, we introduce the classes of $alpha$ and strictly-$alpha$ seminearrings and establishes some of their properties, mostly in relation to the possession of a mate function. Then we get the criterion for an $alpha$-seminearring to become a strictly-$alpha$ seminearring. We also obtain a complete characterisations of $alpha$ and strictly-$alpha$ seminearrings and proved certain results for $alpha$ and strictly-$alpha$ seminearrings via certain unique classes of seminearrings.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"17 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139317629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Automorphism-invariant multiplication modules over a noncommutative ring 论非交换环上的自变不变乘法模块
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-10-05 DOI: 10.24330/ieja.1411145
L. Thuyet, T. C. Quynh
{"title":"On Automorphism-invariant multiplication modules over a noncommutative ring","authors":"L. Thuyet, T. C. Quynh","doi":"10.24330/ieja.1411145","DOIUrl":"https://doi.org/10.24330/ieja.1411145","url":null,"abstract":"One of the important classes of modules is the class of multiplication modules over a commutative ring. This topic has been considered by many authors and numerous results have been obtained in this area. After that, Tuganbaev also considered the multiplication module over a noncommutative ring. In this paper, we continue to consider the automorphism-invariance of multiplication modules over a noncommutative ring. We prove that if $R$ is a right duo ring and $M$ is a multiplication, finitely generated right $R$-module with a generating set ${m_1, dots , m_n}$ such that $r(m_i) = 0$ and $[m_iR: M] subseteq C(R)$ the center of $R$, then $M$ is projective. Moreover, if $R$ is a right duo, left quasi-duo, CMI ring and $M$ is a multiplication, non-singular, automorphism-invariant, finitely generated right $R$-module with a generating set ${m_1, dots , m_n}$ such that $r(m_i) = 0$ and $[m_iR: M] subseteq C(R)$ the center of $R$, then $M_R cong R$ is injective.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"13 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139323334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dimension of uncountably generated submodules 不可数生成子模块的维度
International Electronic Journal of Algebra Pub Date : 2023-08-21 DOI: 10.24330/ieja.1385180
Maryam DAVOUDİAN
{"title":"Dimension of uncountably generated submodules","authors":"Maryam DAVOUDİAN","doi":"10.24330/ieja.1385180","DOIUrl":"https://doi.org/10.24330/ieja.1385180","url":null,"abstract":"In this article we introduce and study the concepts of uncountably generated Krull dimension and uncountably generated Noetherian dimension of an $R$-module, where $R$ is an arbitrary associative ring. These dimensions are ordinal numbers and extend the notion of Krull dimension and Noetherian dimension.
 They respectively rely on the behavior of descending and ascending chains of uncountably generated submodules.
 It is proved that a quotient finite dimensional module $M$ has uncountably generated Krull dimension if and only if it has Krull dimension, but
 the values of these dimensions might differ.
 Similarly, a quotient finite dimensional module $M$ has uncountably generated Noetherian dimension if and only if it has Noetherian dimension.
 We also show that the Noetherian dimension of a quotient finite dimensional module $M$ with uncountably generated Noetherian dimension $beta$ is less than or equal to $omega _{1}+beta $, where $omega_{1}$ is the first uncountable ordinal number.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135875935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pseudo-absorbing comultiplication modules over a pullback ring 回拉环上的伪吸收乘法模块
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-07-26 DOI: 10.24330/ieja.1404416
S. E. Atani, M. Khoramdel, Saboura DOLATİ PİSHHESARİ
{"title":"Pseudo-absorbing comultiplication modules over a pullback ring","authors":"S. E. Atani, M. Khoramdel, Saboura DOLATİ PİSHHESARİ","doi":"10.24330/ieja.1404416","DOIUrl":"https://doi.org/10.24330/ieja.1404416","url":null,"abstract":"In this paper, we introduce the notion of pseudo-absorbing comultiplication modules. A full description of all indecomposable pseudo-absorbing comultiplication modules with finite dimensional top over certain kinds of pullback rings are given and establish a connection between the pseudo-absorbing comultiplication modules and the pure-injective modules over such rings.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139354334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraic Lie Algebra Bundles and Derivations of Lie Algebra Bundles 代数的李代数束和李代数束的衍生
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-07-14 DOI: 10.24330/ieja.1377714
M. V. Moni̇ca, R. Rajendra
{"title":"Algebraic Lie Algebra Bundles and Derivations of Lie Algebra Bundles","authors":"M. V. Moni̇ca, R. Rajendra","doi":"10.24330/ieja.1377714","DOIUrl":"https://doi.org/10.24330/ieja.1377714","url":null,"abstract":"In this paper, we define algebraic Lie algebra bundles, discuss some results on algebraic Lie algebra bundles and derivations of Lie algebra bundles. Some results involving inner derivations and central derivations of Lie algebra bundles are obtained.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":"41 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139359567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE ADE型量子化单李代数BGG范畴中无穷维模的张量积
IF 0.6
International Electronic Journal of Algebra Pub Date : 2023-07-06 DOI: 10.24330/ieja.1357059
Zhaoting Wei̇
{"title":"Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE","authors":"Zhaoting Wei̇","doi":"10.24330/ieja.1357059","DOIUrl":"https://doi.org/10.24330/ieja.1357059","url":null,"abstract":"We consider the BGG category $O$ of a quantized universal enveloping algebra $U_q(mathfrak{g})$. It is well-known that $Motimes Nin O$ if $M$ or $N$ is finite dimensional. When $mathfrak{g}$ is simple and of type ADE, we prove in this paper that $Motimes Nnotin O$ if $M$ and $N$ are both infinite dimensional.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45302004","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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