Title of article :
LOCAL COMPARABILITY OF EXCHANGE IDEALS
Author/Authors :
Kose, Handan Department of Mathematics - Kirsehir Ahi Evran University, Turkey , Kurtulmaz, Yosum Department of Mathematics - Bilkent University Ankara, Turkey
Abstract :
An exchange ideal I of a ring R is locally comparable if for every
regular x ∈ I there exists a right or left invertible u ∈ 1+I such that x = xux.
We prove that every matrix extension of an exchange locally comparable ideal
is locally comparable. We thereby prove that every square regular matrix over
such ideal admits a diagonal reduction.
Keywords :
Locally comparable ideal , matrix extension , diagonal reduction , exchange ideal
Journal title :
International Electronic Journal of Algebra
