an integral dependence in modules over commutative rings
نویسندگان
چکیده
in this paper, we give a generalization of the integral dependence from rings to modules. we study the stability of the integral closure with respect to various module theoretic constructions. moreover, we introduce the notion of integral extension of a module and prove the lying over, going up and going down theorems for modules.
منابع مشابه
AN INTEGRAL DEPENDENCE IN MODULES OVER COMMUTATIVE RINGS
In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.
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عنوان ژورنال:
journal of algebraic systemsناشر: shahrood university of technology
ISSN 2345-5128
دوره 3
شماره 1 2015
کلمات کلیدی
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