### Abstract

The left classical ring of quotients of the polynomial ring Qlcl(R[X]) over an infinite set X is right or left self-injective iff it is quasi-Frobenius iff Qlcl(R) is quasi-Frobenius. The same result holds when X is any nonempty set and Qlcl(R[X]) is right and left self-injective or when Qlcl(R[X]) is injective as a right R[X]-module. Analogous results are given for the classical ring of quotients of a group ring over a free abelian group. As a corollary it is proved that if R is either commutative or right nonsingular then R[X] is right FPF iff X has cardinality one and R is semisimple Artinian. A similar result holds for right FPF group rings over a free abelian group. © 1993.

Original language | English |
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Pages (from-to) | 51-63 |

Journal | Journal of Pure and Applied Algebra |

Volume | 86 |

Issue number | 1 |

DOIs | |

Publication status | Published - 23 Apr 1993 |

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## Cite this

Herbera, D., & Pillay, P. (1993). Injective classical quotient rings of polynomial rings are quasi-Frobenius.

*Journal of Pure and Applied Algebra*,*86*(1), 51-63. https://doi.org/10.1016/0022-4049(93)90152-J