-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 | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1989-0937242-2

Keywords:
Differential identity,
generalized (polynomial) identity,
left (Martindale) quotient ring,
two-sided (Martindale) quotient ring,
prime rings with involution

Article copyright:
© Copyright 1989
American Mathematical Society