Triangular and diagonal forms for matrices over commutative 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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Let R be a noncommutative ring. The zero-divisor graph of R, denoted by Γ(R), is the (directed) graph with vertices Z(R)∗ = Z(R)− {0}, the set of nonzero zero-divisors of R, and for distinct x, y ∈ Z(R)∗, there is an edge x → y if and only if xy = 0. In this paper we investigate the zero-divisor graph of triangular matrix rings over commutative rings. Mathematics Subject Classification: 16S70; ...
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Abstract: A ring R is called a refinement ring if the monoid of finitely generated projective R- modules is refinement. Let R be a commutative refinement ring and M, N, be two finitely generated projective R-nodules, then M~N if and only if Mm ~Nm for all maximal ideal m of R. A rectangular matrix A over R admits diagonal reduction if there exit invertible matrices p and Q such that PAQ is...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1967
ISSN: 0021-8693
DOI: 10.1016/0021-8693(67)90088-9