Köse, H.Kurtulmaz, YosumChen, H.2020-02-052020-02-0520191306-6048http://hdl.handle.net/11693/53078An 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.EnglishDiagonal reductionExchange idealLocally comparable idealMatrix extensionArticle10.24330/ieja.504095