Devamını Göster

Özet

A ring R is uniquely (strongly) clean provided that for any a ∈ R there exists a unique idempotent e ∈ R ( e ∈ comm(a) ) such that a − e ∈ U(R). We prove, in this note, that a ring R is uniquely clean and uniquely bleached if and only if R is abelian, Tn(R) is uniquely strongly clean for all n ≥ 1, i.e. every n × n triangular matrix over R is uniquely strongly clean, if and only if R is abelian, and Tn(R) is uniquely strongly clean for some n ≥ 1. In the commutative case, more explicit results are obtained.

Anahtar Kelimeler

Makale Türü	Özgün Makale
Makale Alt Türü	SSCI, AHCI, SCI, SCI-Exp dergilerinde yayımlanan tam makale
Dergi Adı	Turkish Journal of Mathematics
Dergi ISSN	1300-0098 Wos Dergi Scopus Dergi
Dergi Tarandığı Indeksler	SCI-Expanded
Makale Dili	İngilizce
Basım Tarihi	03-2015
Cilt No	39
Sayfalar	645 / 650
Doi Numarası	10.3906/1408-13

Atıf Sayıları

Uniquely strongly clean triangular matrices

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