Classification of 1-absorbing comultiplication modules over a pullback ring | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 6، دوره 18، شماره 1، اردیبهشت 2023، صفحه 105-129 اصل مقاله (546.03 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.52547/cgasa.2023.103143 | ||
| نویسندگان | ||
| Farkhondeh Farzalipour1؛ Peyman Ghiasvand2 | ||
| 1Department of Mathematics, Payame Noor University, P.O.BOX 19395-3697, Tehran, Iran. | ||
| 2Department of Mathematics, Payame Noor University, P.O.BOX 19395- 3697, Tehran, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| 1-absorbing comultiplication modules؛ Dedekind domains؛ non-separated؛ pure- injective modules؛ pullback؛ separated | ||
| مراجع | ||
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