Geodesic
Noncommutative Prüfer rings
Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 1-8 
N. I. Dubrovin. Noncommutative Prüfer rings. Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/SM_1993_74_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The concept of a Prüfer ring is generalized to orders in simple Artinian rings so that the new concept gives a minimal class of rings closed under Morita equivalence, but in the commutative case does not extend the class of Prüfer domains. In § 1 this problem is solved and some elementary properties of noncommutative Prüfer rings are given. In § 2 theorems on the localization of a noncommutative Prüfer ring with respect to a prime ideal are proved, these being the basis of the theory. In § 3 noncommutative Prüfer rings in a simple finite-dimensional algebra over a field are considered. The main problem, which is posed and partially solved here, involves the connection between a noncommutative Prüfer ring and its center.

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