Classification of 1-absorbing comultiplication modules over a pullback ring

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Farzalipour Farkhondeh; Ghiasvand Peyman

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Journal Paper

Paper Information

Journal: CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS Year:2023 | Volume:18 | Issue:1 Page(s): 105-129

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Information Journal Paper

Title

Classification of 1-absorbing comultiplication modules over a pullback ring

Author(s)

Farzalipour Farkhondeh | Ghiasvand Peyman | Issue Writer Certificate

Keywords

1-absorbing comultiplication modules

Dedekind domains

non-separated

pure-injective modules

pullback

separated

Abstract

One of the aims of the modern representation theory is to solve classification problems for subcategories of modules over a unitary ring R. In this paper, we introduce the concept of 1-absorbing comultiplication modules and classify 1-absorbing comultiplication modules over local Dedekind domains and we study it in detail from the classification problem point of view. The main purpose of this article is to classify all those indecomposable 1-absorbing comultiplication modules with finite-dimensional top over pullback rings of two local Dedekind domains and establish a connection between the 1-absorbing comultiplication modules and the pure-injective modules over such rings. In fact, we extend the definition and results given in [17] to a more general 1-absorbing comultiplication modules case.

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APA: Copy

Farzalipour, Farkhondeh, & Ghiasvand, Peyman. (2023). Classification of 1-absorbing comultiplication modules over a pullback ring. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, 18(1 ), 105-129. SID. https://sid.ir/paper/1057684/en

Vancouver: Copy

Farzalipour Farkhondeh, Ghiasvand Peyman. Classification of 1-absorbing comultiplication modules over a pullback ring. CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS[Internet]. 2023;18(1 ):105-129. Available from: https://sid.ir/paper/1057684/en

IEEE: Copy

Farkhondeh Farzalipour, and Peyman Ghiasvand, “Classification of 1-absorbing comultiplication modules over a pullback ring,” CATEGORIES AND GENERAL ALGEBRAIC STRUCTURES WITH APPLICATIONS, vol. 18, no. 1 , pp. 105–129, 2023, [Online]. Available: https://sid.ir/paper/1057684/en

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