Abstract
By testing quotient rings, we give another viewpoint concerning the relationship between PI and Goldie properties, etc., and f-radical extensions of rings. The main result proved here is as follows: Let R be a prime algebra without nonzero nil right ideals. Suppose that R is f-radical over a subalgebra A, where f (X1, . . . , Xt)is a multilinear polynomial, not an identity for p × p matrices in case char R = p > 0. Suppose that f is not power-central valued in R. Then the maximal ring of right (left) quotients of A coincides with that of R. Moreover, R is right Goldie if and only if A is.
| Original language | English |
|---|---|
| Pages (from-to) | 2933-2944 |
| Number of pages | 12 |
| Journal | Communications in Algebra |
| Volume | 37 |
| Issue number | 9 |
| DOIs | |
| Publication status | Published - 2009 Sep 1 |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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Chuang, C. L., Lee, T. K., & Liu, C-K. (2009). Quotient rings and f-radical extensions of rings. Communications in Algebra, 37(9), 2933-2944. https://doi.org/10.1080/00927870802241170