Diagonal Matrix Reduction over Refinement Rings
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 matri...
Main Authors: | , , |
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Format: | Article |
Language: | fas |
Published: |
Kharazmi University
2022-11-01
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Series: | پژوهشهای ریاضی |
Subjects: | |
Online Access: | http://mmr.khu.ac.ir/article-1-3106-en.html |
Summary: | 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 a diagonal matrix. We also prove that for every refinement ring R, every regular matrix over R admits diagonal reduction if and only if every regular matrix over R/J(R) admits diagonal reduction. |
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ISSN: | 2588-2546 2588-2554 |