Volume 8, Issue 3 (Vol. 8,No. 3, 2022)
mmr 2022, 8(3): 132-143 |
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Sheibani Abdolyousefi M, Bahmani Sangesari R, Ashrafi N. Diagonal Matrix Reduction over Refinement Rings. mmr 2022; 8 (3) :132-143
URL: http://mmr.khu.ac.ir/article-1-3106-en.html
URL: http://mmr.khu.ac.ir/article-1-3106-en.html
1- Women's university of Semnan(Farzanegan) , sheibani@fgusem.ac.ir
2- Semnan university
2- Semnan university
Abstract: (1584 Views)
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.
Type of Study: S |
Subject:
alg
Received: 2020/06/29 | Revised: 2023/06/18 | Accepted: 2021/02/7 | Published: 2022/12/20 | ePublished: 2022/12/20
Received: 2020/06/29 | Revised: 2023/06/18 | Accepted: 2021/02/7 | Published: 2022/12/20 | ePublished: 2022/12/20
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