On S-Semistar-Noetherian Domains

Abstract

Abstract. Let D be an integral domain and S be a multiplicative subset of D. Then given a semistar operation on D, we introduced the S-˜ -Noetherian domains, where˜ is the stable semistar operation of finite type associated to . Among other things, we provide many different characterization for S-˜ -Noetherian domains by focusing on primary decomposition, weak Bourbaki associated primes and Zariski-Samuel associated primes of the S-saturation of a given quasi-˜ -ideal I of D.Mathematics Subject Classification (2010): 13A15, 13F05, 13G05

S-Strongly Finite Type Rings

“…In this work R is a commutative ring with identity, I is an ideal and S is a multiplicative (closed under multiplication) subset of R whose elements are regular. Many classic concepts from ideal theory are generalized to S-concepts for instance see [1], [2], [3], [4], [5]. In [6], Anderson et al defined the ideal I to be an S-finite ideal, if there exists an element s of S and a finitely generated ideal J satisfying: sI ⊆ J ⊆ I.…”