%0 Journal Article
%A Sheibani Abdolyousefi, Marjan
%A Bahmani Sangesari, Raham
%A Ashrafi, Nahid
%T Diagonal Matrix Reduction over Refinement Rings
%J Journal title
%V 8
%N 3
%U http://mmr.khu.ac.ir/article-1-3106-en.html
%R
%D 2022
%K refinement, projective, exchange, diagonal reduction, regular,
%X 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.
%> http://mmr.khu.ac.ir/article-1-3106-en.pdf
%P 132-143
%& 132
%!
%9 S
%L A-10-244-1
%+ Women's university of Semnan(Farzanegan)
%G eng
%@
%[ 2022