Diagonal Matrix Reduction over Refinement Rings

• Published in: پژوهش‌های ریاضی Vol. 8; no. 3; pp. 132 - 143
• Main Authors: Marjan Sheibani Abdolyousefi, Raham Bahmani Sangesari, Nahid Ashrafi
• Format: Journal Article
• Language: Persian
• Published: Kharazmi University 01.11.2022
• Subjects: diagonal reduction; exchange; projective; refinement; regular

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...