On the existence of unimodular elements and cancellation of projective modules over noetherian and non-noetherian rings
نویسندگان
چکیده
منابع مشابه
NONNIL-NOETHERIAN MODULES OVER COMMUTATIVE RINGS
In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...
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We are mainly concerned with the completablity of unimodular rows to an invertible matrix. We first relate this to stable range of the ring. Further, we consider rows generating an idempotent of the ring to obtain completability under special conditions. We try to obtain analogues of important theorems regarding unimodular rows in the case of these “idempotent rows”. By ring, we shall always me...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2016
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2015.09.009