On 2-absorbing submodules and their Amalgamations

2025/10/10 by Gunduz, Abuzer
#13C13 #13C99 #16P60 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.09863

Abstract

Let R₁ and R₂ be commutative rings with 1≠ 0, M and N be unitary R₁-module and R₂-module, respectively. f:R₁→ R₂ be a ring homomorphism and φ: M→ N be an R-module homomorphism. This article studied 2-absorbing submodule that is a generalization of the concept of prime submodule. Firstly, some characterizations of 2-absorbing submodule are presented. Then, we examine the notion of 2-absorbing submodule in amalgamation module M \bowtie^φ JN. We detected when F\bowtie^φJN is a 2-absorbing submodule of M \bowtie^φ JN by using the isomorphism (M \bowtie^φ JN)/(F \bowtie^φ JN) ≅ (M)/(F) and the homomorphism p_γ: M \bowtie^φ JN → φ(M)+JN, where J be an ideal of R₂ and F be a submodule of M.

Citations

• On weakly S-prime submodules
• Properties of chains of prime ideals in an amalgamated algebra along an\n ideal
• Amalgamated algebras along an ideal
• An amalgamated duplication of a ring along an ideal: the basic properties

Related

• On 2-absorbing primary submodules of modules over commutative rings
• Classical 2-absorbing submodules of modules over commutative rings
• 2-absorbing and strongly 2-absorbing secondary submodules of modules
• On 1-absorbing prime submodules
• S-2-absorbing submodules and S-2-absorbing second submodules