Left annihilators characterized by GPIs

Author:
Tsiu Kwen Lee

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3159-3165

MSC:
Primary 16R50; Secondary 16N60

MathSciNet review:
1286000

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Abstract: Let be a semiprime ring with extended centroid , the right Utumi quotient ring of , a subring of containing and , two right ideals of . In the paper we show that if and only if and satisfy the same generalized polynomial identities (GPIs) with coefficients in , where denotes the left annihilator of in . As a consequence of the result, if is a right ideal of such that , then and satisfy the same GPIs with coefficients in the two-sided Utumi quotient ring of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1286000-3

Keywords:
Semiprime ring,
prime ring,
Utumi quotient ring,
GPI,
orthogonal completion

Article copyright:
© Copyright 1995
American Mathematical Society