differential identities of prime rings with involution
Author:
ChenLian Chuang
Journal:
Trans. Amer. Math. Soc. 316 (1989), 251279
MSC:
Primary 16A28; Secondary 16A12, 16A38, 16A72
MathSciNet review:
937242
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Abstract: Main Theorem. Let be a prime ring with involution . Suppose that is a differential identity for , where are distinct regular words of derivations in a basis with respect to a linear order on . Then is a generalized identity for , where are distinct indeterminates. Along with the Main Theorem above, we also prove the following: Proposition 1. Suppose that is of the second kind and that is infinite. Then is special. Proposition 2. Suppose that . Then , the twosided quotient ring of , is equal to . Proposition 3 (Density theorem). Suppose that and are dual spaces with respect to the nondegenerate bilinear form . Let and be such that is independent in and is independent in . Then there exists such that and if and only if for and . Proposition 4. Suppose that is a prime ring with involution and that is a generalized polynomial. If vanishes on a nonzero ideal of , than vanishes on , the twosided quotient ring of .
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947198909372422
PII:
S 00029947(1989)09372422
Keywords:
Differential identity,
generalized (polynomial) identity,
left (Martindale) quotient ring,
twosided (Martindale) quotient ring,
prime rings with involution
Article copyright:
© Copyright 1989
American Mathematical Society
