Pub Date : 2024-09-17DOI: 10.1080/00927872.2024.2398623
Mohamed Chhiti, Hwankoo Kim, Salah Eddine Mahdou
In this paper, we introduce and explore a category of rings termed SFP-rings, defined by the property that each S-finite ideal of them is projective. We demonstrate that all hereditary rings inhere...
{"title":"Commutative rings in which every S-finite ideal is projective","authors":"Mohamed Chhiti, Hwankoo Kim, Salah Eddine Mahdou","doi":"10.1080/00927872.2024.2398623","DOIUrl":"https://doi.org/10.1080/00927872.2024.2398623","url":null,"abstract":"In this paper, we introduce and explore a category of rings termed SFP-rings, defined by the property that each S-finite ideal of them is projective. We demonstrate that all hereditary rings inhere...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258272","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-17DOI: 10.1080/00927872.2024.2398629
D. I. Vladeva
The circle composition e1°e2=e1+e2−e1e2 is well-known from the seminal book of Jacobson. A part of our motivation aims to find non-orthogonal idempotents e1 and e2 such that e1°e2 is an idempotent....
{"title":"The role of semicentral idempotents in triangular matrix rings","authors":"D. I. Vladeva","doi":"10.1080/00927872.2024.2398629","DOIUrl":"https://doi.org/10.1080/00927872.2024.2398629","url":null,"abstract":"The circle composition e1°e2=e1+e2−e1e2 is well-known from the seminal book of Jacobson. A part of our motivation aims to find non-orthogonal idempotents e1 and e2 such that e1°e2 is an idempotent....","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142258270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-12DOI: 10.1080/00927872.2024.2398632
Gary L. Peterson, Stuart D. Scott
When N is a left nearring with identity satisfying the descending chain condition on right ideals N can be written as a direct sum of nonzero right ideals that cannot be further decomposed into dir...
当 N 是一个左近环，其特征满足右理想的降序链条件时，N 可以写成非零右理想的直接和，而这些非零右理想不能进一步分解成方向...
{"title":"Right ideal decompositions of nearrings with faithful 2-step modules","authors":"Gary L. Peterson, Stuart D. Scott","doi":"10.1080/00927872.2024.2398632","DOIUrl":"https://doi.org/10.1080/00927872.2024.2398632","url":null,"abstract":"When N is a left nearring with identity satisfying the descending chain condition on right ideals N can be written as a direct sum of nonzero right ideals that cannot be further decomposed into dir...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-11DOI: 10.1080/00927872.2024.2395975
José Manuel Fernández Vilaboa, Ramón González Rodríguez, Brais Ramos Pérez
The present article is devoted to introduce the notion of Hopf bracoid in the braided monoidal framework as the quantum version of skew bracoids, which have been presented by Martin-Lyons and Truma...
本文专门介绍了编单体框架中的霍普夫辫状体概念，它是偏斜辫状体的量子版本，由马丁-里昂和特鲁马提出。
{"title":"Hopf bracoids","authors":"José Manuel Fernández Vilaboa, Ramón González Rodríguez, Brais Ramos Pérez","doi":"10.1080/00927872.2024.2395975","DOIUrl":"https://doi.org/10.1080/00927872.2024.2395975","url":null,"abstract":"The present article is devoted to introduce the notion of Hopf bracoid in the braided monoidal framework as the quantum version of skew bracoids, which have been presented by Martin-Lyons and Truma...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"45 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-07DOI: 10.1080/00927872.2024.2395707
Laura Capuano, Marzio Mula, Lea Terracini
We develop a theory of p-adic continued fractions for a quaternion algebra B over Q ramified at a rational prime p. Many properties holding in the commutative case can be proven also in this settin...
我们为在有理素数 p 处斜切的 Q 上的四元数代数 B 建立了 p-adic 续分理论。
{"title":"Quaternionic p-adic continued fractions","authors":"Laura Capuano, Marzio Mula, Lea Terracini","doi":"10.1080/00927872.2024.2395707","DOIUrl":"https://doi.org/10.1080/00927872.2024.2395707","url":null,"abstract":"We develop a theory of p-adic continued fractions for a quaternion algebra B over Q ramified at a rational prime p. Many properties holding in the commutative case can be proven also in this settin...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-06DOI: 10.1080/00927872.2024.2395988
Jun Dong, Jie Wei
Let R be a ring such that all flat R-modules have finite strongly FP-injective dimension. We obtain that the class of all Gorenstein projective modules forms a left-hand class of complete and hered...
假设 R 是一个环，所有平 R 模块都具有有限的强 FP 注入维度。我们得到，所有戈伦斯坦射影模块的类构成了一个完整且有嗣的左手类。
{"title":"Gorenstein projective and weak Gorenstein flat modules","authors":"Jun Dong, Jie Wei","doi":"10.1080/00927872.2024.2395988","DOIUrl":"https://doi.org/10.1080/00927872.2024.2395988","url":null,"abstract":"Let R be a ring such that all flat R-modules have finite strongly FP-injective dimension. We obtain that the class of all Gorenstein projective modules forms a left-hand class of complete and hered...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-05DOI: 10.1080/00927872.2024.2394969
David A. Towers
This paper starts by showing that, for algebras in a certain class, the concepts of weak nilpotency and nilpotency coincide. It goes on to describe some solvability and nilpotency properties of bic...
{"title":"Nilpotency, solvability and Frattini theory for bicommutative, assosymmetric and Novikov algebras","authors":"David A. Towers","doi":"10.1080/00927872.2024.2394969","DOIUrl":"https://doi.org/10.1080/00927872.2024.2394969","url":null,"abstract":"This paper starts by showing that, for algebras in a certain class, the concepts of weak nilpotency and nilpotency coincide. It goes on to describe some solvability and nilpotency properties of bic...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206039","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1080/00927872.2024.2393693
Antonio Lanteri, Raquel Mallavibarrena
Rational conic fibrations embedded in PN and containing an irreducible curve C transverse to the fibers are classified when C is either a plane curve or a rational normal curve of any degree d. Th...
当 C 为平面曲线或任意度 d 的有理法向曲线时，嵌入 PN 且包含横向于纤维的不可还原曲线 C 的有理圆锥纤维被分类。
{"title":"Rational conic fibrations containing special curves transverse to the fibers","authors":"Antonio Lanteri, Raquel Mallavibarrena","doi":"10.1080/00927872.2024.2393693","DOIUrl":"https://doi.org/10.1080/00927872.2024.2393693","url":null,"abstract":"Rational conic fibrations embedded in PN and containing an irreducible curve C transverse to the fibers are classified when C is either a plane curve or a rational normal curve of any degree d. Th...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"6 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-03DOI: 10.1080/00927872.2024.2392010
P. Bhattacharjee, W.Wm. McGovern, Y. Zhou
A ring is called left fusible if each of its nonzero elements is the sum of a left zero-divisor and a non-left zero-divisor. This paper aims to extend the existing theory of left fusible rings and ...
{"title":"On fusible rings and related notions","authors":"P. Bhattacharjee, W.Wm. McGovern, Y. Zhou","doi":"10.1080/00927872.2024.2392010","DOIUrl":"https://doi.org/10.1080/00927872.2024.2392010","url":null,"abstract":"A ring is called left fusible if each of its nonzero elements is the sum of a left zero-divisor and a non-left zero-divisor. This paper aims to extend the existing theory of left fusible rings and ...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"16 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-02DOI: 10.1080/00927872.2024.2395974
S. N. Arjun, P. G. Romeo
Batten introduced the concept of a cover for Lie algebras in [3]. In this article, we describe the irreducible representation of cover of Lie algebras by establishing a bijective correspondence bet...
Batten 在[3]中引入了李代数的盖的概念。在本文中，我们将通过在......与......
{"title":"On irreducible representation of cover of Lie algebras","authors":"S. N. Arjun, P. G. Romeo","doi":"10.1080/00927872.2024.2395974","DOIUrl":"https://doi.org/10.1080/00927872.2024.2395974","url":null,"abstract":"Batten introduced the concept of a cover for Lie algebras in [3]. In this article, we describe the irreducible representation of cover of Lie algebras by establishing a bijective correspondence bet...","PeriodicalId":50663,"journal":{"name":"Communications in Algebra","volume":"25 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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