Maximal quotients of semiprime PI-algebras
Author:
Louis Halle Rowen
Journal:
Trans. Amer. Math. Soc. 196 (1974), 127-135
MSC:
Primary 16A38
DOI:
https://doi.org/10.1090/S0002-9947-1974-0347887-8
MathSciNet review:
0347887
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Abstract | References | Similar Articles | Additional Information
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 of R. In this paper we characterize
in terms of essential ideals of C = cent R. This permits immediate reduction of many facets of
to the commutative case, yielding some new results and some rapid proofs of known results. Direct product decompositions of
are given, and
turns out to have an involution when R has an involution.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1974-0347887-8
Keywords:
Essential,
identity,
injective hull,
involution,
maximal quotient algebra,
PI-algebra,
semiprime,
singular ideal
Article copyright:
© Copyright 1974
American Mathematical Society