When Socles Split in Injectivity Domains of Modules

Atani, Shahabaddin Ebrahimi; Khoramdel, Mehdi; Hesari, Saboura Dolati Pish

doi:10.1007/s00009-023-02359-5

“…Since the inception of rings with no middle class in 2010, there has been a growing research interest in examining rings by imposing restrictions on the injectivity domains of their modules. In [3,4,5,7,10,19,20], rings whose modules are of restricted domains of injectivity are studied. Each of these papers is interested in when modules are either injective or far from being injective to a specified degree.…”

Section: Introductionmentioning

confidence: 99%

“…In [3], rings with local profiles whose unique coatom consists of all semiartinian modules are characterized. In [4], rings with local profiles whose unique coatom consists of all locally Noetherian V-modules are discussed. Also, in [7], rings with local profiles whose unique coatom is the class of all V-modules are considered.…”

Section: Introductionmentioning

confidence: 99%

On the Splitting Property of Rings with Restricted Class of Injectivity Domains

Saraç

2023

Preprint

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There has been a growing research interest in exploring rings whose modules are either injective or far from being injective to a specified degree. As is commonly observed in each of such scenarios, rings can be broken as a direct sum, where one of the two components is a semisimple Artinian ring and the other is an indecomposable ring having zero or (essential) homogeneous right socle. Although this phenomenon has become increasingly expected and less surprising with every new study, proving it has never become easier, and in most cases, it has been obtained as a result of considerable efforts. This work aims to bring such studies to a common denominator and tries to explain why this phenomenon occurs each time we deal with the same type of problem. Mathematics Subject Classification. Primary 16D50; Secondary 16S90, 16N60

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On subprojective portfolios of modules

Durğun,

Shibeshi

2024

Indian J Pure Appl Math

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On the splitting property of rings with restricted class of injectivity domains

Saraç

2024

Communications in Algebra

0

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There has been a growing research interest in exploring rings whose modules are either injective or far from being injective to a specified degree. As is commonly observed in each of such scenarios, rings can be broken as a direct sum, where one of the two components is a semisimple Artinian ring and the other is an indecomposable ring having zero or (essential) homogeneous right socle. Although this phenomenon has become increasingly expected and less surprising with every new study, proving it has never become easier, and in most cases, it has been obtained as a result of considerable efforts. This work aims to bring such studies to a common denominator and tries to explain why this phenomenon occurs each time we deal with the same type of problem.

show abstract

When Socles Split in Injectivity Domains of Modules

Cited by 4 publications

References 23 publications

On the Splitting Property of Rings with Restricted Class of Injectivity Domains

On the Splitting Property of Rings with Restricted Class of Injectivity Domains

On subprojective portfolios of modules

On the splitting property of rings with restricted class of injectivity domains

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