Right unique factorization domains
The author's aim is to study a notion of one-sided unique factorization domain (UFD) which is stronger than the similarity-UFD defined by \textit{P. M. Cohn} [Am. Math. Mon. 80, 1-18 (1973; Zbl 0256.13011)] but reduces to the usual form in the commutative case. A right-UFD is defined as an atomic integral domain such that for any two complete factorizations of an element, \(c = a_ 1 \dots a_ m = b_ 1 \dots b_ n\), where \(a_ i\), \(b_ j\) are atoms, one has \(m = n\) and for some permutation \(\pi\) of \(1,\dots,n\), \(a_ i\) is right associated to \(b_{\pi(i)}\). For a right invariant ring, being a right-UFD is shown to be equivalent to being a similarity-UFD, but an example shows that such a ring need not be a left- UFD (defined correspondingly); however, this does follow if the ring is also left Ore.
scientific article; zbMATH DE number 645214