### 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 (X_{1}, . . . , X_{t})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 |
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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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## Cite this

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