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