Geodesic
Elementary Factorization in π-Regular Rings
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 307-313

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

This paper extends the results of A. L. Foster (1) on elementary factorization in Boolean-like rings to commutative π-regular rings. After proving some preliminary lemmas we proceed to the partition of the set of non-units of a π-regular ring into irreducible and composite elements. Finally, we prove a number of theorems concerning factorization rings, weakly unique factorization rings, principal ideal rings, etc. The principal result is that a π-regular ring is a weakly unique factorization ring if and only if it is a principal ideal ring. 
Steger, Arthur. Elementary Factorization in π-Regular Rings. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 307-313. doi: 10.4153/CJM-1966-034-6
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