2021/07/02 by Khashan, Hani, Celikel, Ece Yetkin
#13A15 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2107.00970
Let R be a commutative ring with identity and S a multiplicatively closed subset of R. This paper aims to introduce the concept of S-n-ideals as a generalization of n-ideals. An ideal I of R disjoint with S is called an S-n-ideal if there exists s∈ S such that whenever ab∈ I for a,b∈ R, then sa∈√(0) or sb∈ I. The relationship among S% -n-ideals, n-ideals, S-prime and S-primary ideals are clarified. Several properties, characterizations and examples are presented such as investigating S-n-ideals under various contexts of constructions including direct products, localizations and homomorphic images. Furthermore, for m∈% %TCIMACRO\U2115 % %BeginExpansion ℕ %EndExpansion and some particular S, all S-n-ideals of the ring % %TCIMACRO\U2124 % %BeginExpansion ℤ %EndExpansion m are completely determined. The last section is devoted for studying the S-n-ideals of the idealization ring and amalgamated algebra.