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Structure of a Certain Class of Rings with Involution

Published online by Cambridge University Press:  20 November 2018

M. Chacron ,
I. N. Herstein  and
S. Montgomery
M. Chacron
Affiliation:
Carleton University, Ottawa, Ontario
I. N. Herstein
Affiliation:
University of Chicago, Chicago, Illinois
S. Montgomery
Affiliation:
University of Southern California, Los Angeles, California
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Let R be a ring with involution *, and let Z denote the center of R. In R let S = {x ∈ R|x* = x} be the set of symmetric elements of R. We shall study rings which are conditioned in the following way: given s ∈ S, then for some integer and some polynomial p(t), with integer coefficients which depend on . What can one hope to say about such rings? Certainly all rings in which every symmetric element is nilpotent fall into this class.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 5 , 01 October 1975 , pp. 1114 - 1126
Copyright
Copyright © Canadian Mathematical Society 1975

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