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Transactions of the American Mathematical Society

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Regular self-injective rings with a polynomial identity


Authors: Efraim P. Armendariz and Stuart A. Steinberg
Journal: Trans. Amer. Math. Soc. 190 (1974), 417-425
MSC: Primary 16A38
DOI: https://doi.org/10.1090/S0002-9947-1974-0354763-3
MathSciNet review: 0354763
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Abstract: This paper studies maximal quotient rings of semiprime P. I.-rings; such rings are regular, self-injective and satisfy a polynomial identity. We show that the center of a regular self-injective ring is regular self-injective; this enables us to establish that the center of the maximal quotient ring of a semiprime P. I.-ring R is the maximal quotient ring of the center of R, as well as some other relationships. We give two decompositions of a regular self-injective ring with a polynomial identity which enable us to show that such rings are biregular and are finitely generated projective modules over their center.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0354763-3
Keywords: von Neumann regular, semiprime ring, polynomial identity, maximal quotient ring, center of a ring
Article copyright: © Copyright 1974 American Mathematical Society

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