Geodesic
Semicritical Rings and the Quotient Problem
Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 160-170

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

The purpose of this paper is to examine the relationship between the quotient problem for right noetherian nonsingular rings and the quotient problem for semicritical rings. It is shown that a right noetherian nonsingular ring R has an artinian classical quotient ring iff certain semicritical factor rings R/K i , i = 1,...,n, possess artinian classical quotient rings and regular elements in R/K i lift to regular elements of R for all i. If R is a two sided noetherian nonsingular ring, then the existence of an artinian classical quotient ring is equivalent to each R/Ki possessing an artinian classical quotient ring and the right Krull primes of R consisting of minimal prime ideals. If R is also weakly right ideal invariant, then the former condition is redundant. Necessary and sufficient conditions are found for a nonsingular semicritical ring to have an artinian classical quotient ring.
DOI : 10.4153/CMB-1984-025-7
Mots-clés : 16A46, 16A66, 16A55 
Kosler, Karl A. Semicritical Rings and the Quotient Problem. Canadian mathematical bulletin, Tome 27 (1984) no. 2, pp. 160-170. doi: 10.4153/CMB-1984-025-7
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