On Modules Satisfying S-Noetherian Spectrum Condition  

作　　者：MehmetÖzen Osama A.Naji Ünsal Tekir Suat Koç 

机构地区：[1]Department of Mathematics,Sakarya University,Sakarya,Turkey [2]Department of Mathematics,Marmara University,Istanbul,Turkey

出　　处：《Communications in Mathematics and Statistics》2023年第3期649-662,共14页数学与统计通讯（英文）

摘　　要：Let R be a commutative ring having nonzero identity and M be a unital R-module.Assume that S⊆R is a multiplicatively closed subset of R.Then,M satisfies S-Noetherian spectrum condition if for each submodule N of M,there exist s∈S and afinitely generated submodule F⊆N such that sN⊆radM(F),where radM(F)is the prime radical of F in the sense(McCasland and Moore in Commun Algebra 19(5):1327–1341,1991).Besides giving many properties and characterizations of S-Noetherian spectrum condition,we prove an analogous result to Cohen’s theorem for modules satisfying S-Noetherian spectrum condition.Moreover,we characterize modules having Noetherian spectrum in terms of modules satisfying the S-Noetherian spectrum condition.

关 键 词：Noetherian modules S-Noetherian modules Noetherian spectrum S-Noetherian spectrum condition 

分 类 号：O15[理学—数学]