FP-injective and weakly quasi-Frobenius rings

Details FP-injective and weakly quasi-Frobenius rings FP-injective and weakly quasi-Frobenius rings

1999-11-18

arxiv.org/abs/math/9911137v2

Zapiski Nauchnykh Seminarov POMI, vol. 265 (in Russian). English transl. in Journal of Math. Sciences

Mathematics

Rings and Algebras

AMSLatex, 15 pages

Scientific paper

The classes of FP-injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in fp-flat and free modules respectively. Using these properties, we describe the classes of coherent CF and FGF-rings. Moreover, it is proved that the group ring R(G) is FP-injective (resp. weakly quasi-Frobenius) if and only if the ring R is FP-injective (resp. weakly quasi-Frobenius) and the group G is locally finite.

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