## Regular self-injective rings with a polynomial identity

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- by Efraim P. Armendariz and Stuart A. Steinberg PDF
- Trans. Amer. Math. Soc.
**190**(1974), 417-425 Request permission

## 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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## Additional Information

- © Copyright 1974 American Mathematical Society
- 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