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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Maximal quotients of semiprime PI-algebras

Author: Louis Halle Rowen
Journal: Trans. Amer. Math. Soc. 196 (1974), 127-135
MSC: Primary 16A38
MathSciNet review: 0347887
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Abstract: J. Fisher [3] initiated the study of maximal quotient rings of semiprime PI-rings by noting that the singular ideal of any semiprime Pi-ring R is 0; hence there is a von Neumann regular maximal quotient ring $ Q(R)$ of R. In this paper we characterize $ Q(R)$ in terms of essential ideals of C = cent R. This permits immediate reduction of many facets of $ Q(R)$ to the commutative case, yielding some new results and some rapid proofs of known results. Direct product decompositions of $ Q(R)$ are given, and $ Q(R)$ turns out to have an involution when R has an involution.

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Keywords: Essential, identity, injective hull, involution, maximal quotient algebra, PI-algebra, semiprime, singular ideal
Article copyright: © Copyright 1974 American Mathematical Society