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Orders in simple Artinian rings are strongly equivalent to matrix rings

Julius Zelmanowitz
1973 Pacific Journal of Mathematics  
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 {e^ } for Q and an element reD, where D is the intersection of the centralizer of {e^ } with R, such that rRr Q £ De v and Σ rDe v = 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
more » ... er C in the centralizer of {e^} which inherits the corresponding property of R and such that R is equivalent to the matrix ring ^ Cβij.
doi:10.2140/pjm.1973.48.621 fatcat:aqzgdiaxybernab7dsdqtlw74y