Geodesic
Unique factorisation of normal elements in non-commutative rings
Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 103-113

Voir la notice de l'article provenant de la source Cambridge University Press

In the literature there are several generalisations to non-commutative rings of the notion of a unique factorisation domain from commutative algebra. This paper follows in the spirit of [1, 3] and is set in the context of Noetherian rings. In [3], A. W. Chatters and the author denned a Noetherian UFR (unique factorisation ring) to be a prime Noetherian ring R in which every non-zero prime ideal contains a prime ideal generated by a non-zero normal element p, that is, by an element p such that pR = Rp. The class of Noetherian UFRs includes the Noetherian UFDs studied by Chatters in [1], while a commutative Noetherian ring is a UFR if and only if it is a UFD in the usual sense. For a Noetherian UFR R, the following are simple consequences of the definition:(i) every non-zero ideal of R contains a non-zero normal element;(ii) the set N(R) of non-zero normal elements of R is a unique factorisation monoid in the sense of [4, Chapter 3]. 
Jordan, D. A. Unique factorisation of normal elements in non-commutative rings. Glasgow mathematical journal, Tome 31 (1989) no. 1, pp. 103-113. doi: 10.1017/S001708950000759X
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