Diagonal Matrix Reduction over Refinement Rings

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...

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Bibliographic Details
Published inپژوهش‌های ریاضی Vol. 8; no. 3; pp. 132 - 143
Main Authors Marjan Sheibani Abdolyousefi, Raham Bahmani Sangesari, Nahid Ashrafi
Format Journal Article
LanguagePersian
Published Kharazmi University 01.11.2022
Subjects
diagonal reduction
exchange
projective
refinement
regular
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Summary: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.
ISSN:2588-2546
2588-2554