Geodesic
Noncommutative Pr\"ufer rings
Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 1-8

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. 
@article{SM_1993_74_1_a0,
     author = {N. I. Dubrovin},
     title = {Noncommutative {Pr\"ufer} rings},
     journal = {Sbornik. Mathematics},
     pages = {1--8},
     publisher = {mathdoc},
     volume = {74},
     number = {1},
     year = {1993},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1993_74_1_a0/}
}
TY  - JOUR
AU  - N. I. Dubrovin
TI  - Noncommutative Pr\"ufer rings
JO  - Sbornik. Mathematics
PY  - 1993
SP  - 1
EP  - 8
VL  - 74
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1993_74_1_a0/
LA  - en
ID  - SM_1993_74_1_a0
ER  - 
%0 Journal Article
%A N. I. Dubrovin
%T Noncommutative Pr\"ufer rings
%J Sbornik. Mathematics
%D 1993
%P 1-8
%V 74
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1993_74_1_a0/
%G en
%F SM_1993_74_1_a0
N. I. Dubrovin. Noncommutative Pr\"ufer rings. Sbornik. Mathematics, Tome 74 (1993) no. 1, pp. 1-8. http://geodesic.mathdoc.fr/item/SM_1993_74_1_a0/