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Diagonal Matrix Reduction over Refinement Rings
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| Marjan Sheibani Abdolyousefi1, Raham Bahmani Sangesari2, Nahid Ashrafi2 |
1- Women's university of Semnan(Farzanegan) , sheibani@fgusem.ac.ir
2- Semnan university |
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Abstract: (120 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.
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| Keywords: refinement, projective, exchange, diagonal reduction, regular |
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Full-Text [PDF 1284 kb]
(44 Downloads)
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Type of Study: S |
Subject:
alg
Received: 2020/06/29 | Revised: 2023/01/4 | Accepted: 2021/02/7 | Published: 2022/12/20 | ePublished: 2022/12/20
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