2020/06/17 by Emel Aslankarayiğit Uğurlu, Ugurlu, Emel Aslankarayigit
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2006.09371
openalex publication_date 2020/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Throughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of ϕ-prime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the set of all submodules of M and ϕ:S(M)→ S(M)∪\∅\ is a function. For every Y∈ S(M) and ideal I of R, a proper submodule X of M is called ϕ-prime, if YI⊆ X and YI\nsubseteqϕ(X), then Y⊆ X or I⊆(X:RM). Then we examine the properties of ϕ-prime submodules and characterize it when M is a multiplication module.