Vol. 48, No. 2, 1973

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Orders in simple Artinian rings are strongly equivalent to matrix rings

Julius Martin Zelmanowitz

Vol. 48 (1973), No. 2, 621–627

The result indicated by the title will be proved. More specifically stated: when R is a left order in a simple artinian ring Q, there exist matrix units {eij} for Q and an element ∕γ D, where D is the intersection of the centralizer of {eij} with R, such that rRr Deij and rDeij R. The Faith-Utumi theorem is an immediate consequence of this relationship. Furthermore, if R is either a maximal order, or is subdirectly irreducible, or is hereditary, then there is a left order C in the centralizer of {eij} which inherits the corresponding property of R and such that R is equivalent to the matrix ring Ceij.

Mathematical Subject Classification
Primary: 16A18
Received: 31 July 1972
Published: 1 October 1973
Julius Martin Zelmanowitz