TY - JOUR
T1 - Diagonal Matrix Reduction over Refinement Rings
TT - قطری پذیری ماتریسها روی حلقهای تظریف پذیر
JF - khu-mmr
JO - khu-mmr
VL - 8
IS - 3
UR - http://mmr.khu.ac.ir/article-1-3106-en.html
Y1 - 2022
SP - 132
EP - 143
KW - refinement
KW - projective
KW - exchange
KW - diagonal reduction
KW - regular
N2 - 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.
M3
ER -