Semi n-submodules of modules over commutative rings

2025/09/10 by Khashan, Hani, Celikel, Ece Yetkin
#13A15 #13A99 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.08397

Abstract

Let R be a commutative ring with identity and M a unitary R-module. The purpose of this paper is to introduce the concept of semi-n-submodules as an extension of semi n-ideals and n-submodules. A proper submodule N of M is called a semi n-submodule if whenever r∈ R, m∈ M with r²m∈ N, r∉√(0) and Ann_R(m)=0, then rm∈ N. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi n-submodules of amalgamated modules are investigated.

Citations

• Semi r-ideals of commutative rings
• Quasi J-ideals of Commutative Rings
• Weakly J-ideals of Commutative Rings
• Properties of chains of prime ideals in an amalgamated algebra along an ideal
• An amalgamated duplication of a ring along an ideal: the basic properties

Related

• Semimodules over commutative semirings and modules over unitary\n commutative rings
• The dual of the notions r-submodules, n-submodules, and J-submodules
• Generalizations of prime submodules over non-commutative rings
• On (k,n)-closed submodules
• n-pure submodules of modules