On classical quotients of polynomial identity rings with involution

Author:
Louis Halle Rowen

Journal:
Proc. Amer. Math. Soc. **40** (1973), 23-29

MSC:
Primary 16A28

DOI:
https://doi.org/10.1090/S0002-9939-1973-0323822-8

MathSciNet review:
0323822

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Abstract: Let denote a ring with involution , where ``involution'' means `` ". We can specialize many ring-theoretical concepts to rings with involution; in particular an *ideal* of is an ideal of stable under , and *the center of* is the set of central elements of which are fixed under . Then we say *is prime* when the product of any two nonzero ideals of is nonzero; similarly *is semiprime* when any power of a nonzero ideal of is nonzero. The main result of this paper is a strong analogue to Posner's theorem [**5**], namely that any prime with polynomial identity has a ring of quotients , formed merely by adjoining inverses of nonzero elements of the center of . This quotient ring is simple and finite dimensional over its center. An extension of these results to semiprime Goldie rings with polynomial identity is given.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1973-0323822-8

Keywords:
Classical ring of quotients,
Goldie ring,
involution,
polynomial identity,
prime,
semiprime,
simple,
center,
central quotients

Article copyright:
© Copyright 1973
American Mathematical Society