Regular self-injective rings with a polynomial identity

Armendariz, Efraim P.; Steinberg, Stuart A.

doi:10.1090/S0002-9947-1974-0354763-3

Regular self-injective rings with a polynomial identity
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by Efraim P. Armendariz and Stuart A. Steinberg

Trans. Amer. Math. Soc. 190 (1974), 417-425

DOI: https://doi.org/10.1090/S0002-9947-1974-0354763-3

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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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Regular rings

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