LOCAL COMPARABILITY OF EXCHANGE IDEALS

Authors : Handan KOSE, Yosum KURTULMAZ, Huanyin CHEN

Pages : 1-11

Doi:10.24330/ieja.504095

View : 14 | Download : 11

Publication Date : 2019-01-08

Article Type : Research Paper

Abstract :An exchange ideal $I$ of a ring $R$ is locally comparable if for every regular $x\in I$ there exists a right or left invertible $u\in 1+I$ 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