New characterizations of pseudo-Frobenius rings and a generalization of the FGF conjecture

Abstract

Abstract. We provide new characterizations of pseudo-Frobenius and quasiFrobenius rings in terms of tight modules. In the process, we also provide fresh perspectives on FGF and CF conjectures. In particular, we propose new natural extensions of these conjectures which connect them with the classical theory of PF rings. Our techniques are mainly based on set-theoretic counting arguments initiated by Osofsky. Several corollaries and examples to illustrate their applications are given.

Modules which are self-p-injective relative to projection invariant submodules

“…Finally, we give examples which show that there is no implication between self-p-injective and tight concepts. Recall that a module M is said to be right tight (resp.,right M -tight) if every finitely generated (resp., cyclic) submodule of E(M ) can be embedded in M (see [1], [6]). …”