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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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 $ R$ be a semiprime ring with extended centroid $ C$, $ U$ the right Utumi quotient ring of $ R$, $ S$ a subring of $ U$ containing $ R$ and $ {\rho _1}$, $ {\rho _2}$ two right ideals of $ R$. In the paper we show that $ {l_S}({\rho _1}) = {l_S}({\rho _2})$ if and only if $ {\rho _1}$ and $ {\rho _2}$ satisfy the same generalized polynomial identities (GPIs) with coefficients in $ SC$, where $ {l_S}({\rho _i})$ denotes the left annihilator of $ {\rho _i}$ in $ S$. As a consequence of the result, if $ \rho $ is a right ideal of $ R$ such that $ {l_R}(\rho ) = 0$, then $ \rho $ and $ U$ satisfy the same GPIs with coefficients in the two-sided Utumi quotient ring of $ R$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1286000-3
PII: S 0002-9947(1995)1286000-3
Keywords: Semiprime ring, prime ring, Utumi quotient ring, GPI, orthogonal completion
Article copyright: © Copyright 1995 American Mathematical Society