On 1-absorbing prime submodules
Emel Aslankarayigit Ugurlu
Department of Mathematics, Marmara University, 34722, Istanbul, Turkey.
Pages 162-173 | Received 06 February 2023, Accepted 17 April 2023, Published 16 June 2023
Abstract
Our aim for this paper is to present the notion of 1-absorbing prime submodules of A-module M. We display that the new notion is a generalization of prime submodules coinciding it is a sort of specialized 2-absorbing submodule. Along with some properties of them, we characterize the quasi local rings by the help ofthe new concept. Also, we investigate their behaviors under homomorphisms, in the localization of modules, and in a cartesian product of modules. After introducing the minimal 1-absorbing prime submodules, the radical_{\text{1}} of ideals and submodules, we obtain some famous results for them. Furthermore, we obtain two characterizations of the concept in a multiplication module. Finally, we obtain a result for 1-absorbing prime submodules similar to the Prime Avoidance Theorem.
Keywords: prime ideal, prime submodule, 1-absorbing prime, prime avoidence theorem.
MSC numbers: Primary 13A15; Secondary 16P40, 16D60.
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