FP-injective and weakly quasi-Frobenius rings

1999/11/30 by Grigory Garkusha
Mathematics · #math.RA #msc:16D #msc:16G

paper · pdf

published as Zapiski Nauchnykh Seminarov POMI, vol. 265 (in Russian). English transl. in Journal of Math. Sciences · AMSLatex, 15 pages

arxiv created 1999/12/30 · arxiv updated 2009/11/30

Abstract

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.

Related

• The Frobenius functor and injective modules
• New Characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture
• Locally Frobenius algebras and Hopf algebras
• Aspects on weak, s-CS and almost injective rings
• Graded Frobenius Rings