ISSN 1088-6850(online) ISSN 0002-9947(print)

-differential identities of prime rings with involution

Author: Chen-Lian Chuang
Journal: Trans. Amer. Math. Soc. 316 (1989), 251-279
MSC: Primary 16A28; Secondary 16A12, 16A38, 16A72
DOI: https://doi.org/10.1090/S0002-9947-1989-0937242-2
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 two-sided 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 two-sided quotient ring of .

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