Phi Classical 1-Absorbing Prime Submodule
Zeynep Y{\i}lmaz U\c{c}ar, Bayram Ali Ersoy, \"Unsal Tekir, Ece Yetkin, \c{C}elikel, and Serkan Onar
TL;DR
This paper introduces the concept of phi classical 1-absorbing prime submodules in commutative rings with identity, providing properties and characterizations of these new submodules.
Contribution
It defines a new class of submodules called phi classical 1-absorbing prime submodules and explores their properties and characterizations.
Findings
Characterization of phi classical 1-absorbing prime submodules
Properties relating to submodule behavior
Conditions under which submodules are phi classical 1-absorbing prime
Abstract
In this paper, all rings are commutative with nonzero identity. Let M be an R-module. We introduce the concept of phi classical 1-absorbing prime submodules. A proper submodule N of M is a phi classical 1-absorbing prime submodule if whenever non units a, b, c belongs to R and m belongs to M with abcm belongs to N and does not belong to phi(N), then abm belongs to N or cm belongs to N. Many properties and characterizations of phi classical 1-absorbing prime submodules are given.
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Taxonomy
TopicsHistory and Theory of Mathematics · Advanced Mathematical Theories · Computability, Logic, AI Algorithms