On S-Integral Domains and S-Version of Krull Intersection Theorem

2025/12/23 by Singh, Tushar, Verma, Gyanendra K., Kumar, Shiv Datt
#12E20 #13G05 #16U10 #16U40 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2512.20316

Abstract

Let S⊆ R be a multiplicatively closed subset of a ring R. We extend several results on integral domains to their S-versions and establish the S-version of Krull intersection theorem. We also show that if R is an S-field, then the localization of R with respect to S is a ϕ(S)-field, where ϕ(S)= \\dfracs1| s∈ S \ is a multiplicatively closed subset of S^-1R, and prove the converse under the condition of finiteness of S. As a consequence, we show that every finite S-integral domain is an S-field. Also, we provide several examples to illustrate the significance of our findings.

Citations

• A Study of S-Primary Decompositions
• On S-strong Mori domains

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