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Structure of Rings with Involution Applied to Generalized Polynomial Identities

Published online by Cambridge University Press:  20 November 2018

Louis Halle Rowen
Louis Halle Rowen*
Affiliation:
University of Chicago, Chicago, Illinois
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In [14, §4], some theorems were obtained about generalized polynomial identities in rings with involution, but the statements had to be weakened somewhat because a structure theory of rings with involution had not yet been developed sufficiently to permit proofs to utilize enough properties of rings with involution. In this paper, such a theory is developed. The key concept is that of the central closure of a ring with involution, given in § 1, shown to have properties analogous to the central closure of a ring without involution. In § 2, the theory of primitive rings with involution, first set forth by Baxter-Martindale [5], is pushed forward, to enable a setting of generalized identities in rings with involution which can parallel the non-involutory situation.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 3 , 01 June 1975 , pp. 573 - 584
Copyright
Copyright © Canadian Mathematical Society 1975

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