Let R be a ring. For a fixed positive integer n, R is said to be left n-semihereditary in case
every n-generated left ideal is projective. R is said to be weakly n-semihereditary if each n …

It is shown that if R is a right automorphism-invariant ring and satisfies ACC on right
annihilators, then R is a semiprimary ring. By this useful fact, we study finiteness conditions …

The concepts of an intrinsically projective module and an intrinsically injective module are
introduced and their connection with the presence of annihilator conditions in the …

A ring R is called right principally injective (right P-injective) if every R-linear map from a
principal right ideal of R can be extended to R. If every ring homomorphic image of R is right …

This paper introduce and investigate the notion of FI− M− principally injective and FI− semi-
injective (fully invariant-semi injective) modules. Clearly FI− semi-injective module does not …

ON SELF-INJECTIVE PERFECT RINGS Page 1 Canad. Math. Bull. Vol. 39 (1), 1996 pp. 55-58
ON SELF-INJECTIVE PERFECT RINGS DOLORS HERBERA AND AHMAD SHAMSUDDIN …

A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Publisher Summary This chapter describes the hereditarily and cohereditarily projective
modules. There is a similarity between the study of n-firs and that of right semihereditary …

In this paper, we introduce the notion of “P-semihereditary”(resp.,“P-hereditary”) rings which
is a generalization of the notion of “semihereditary”(resp.,“hereditary”) rings. Then we …

A module M is called EPI-RETRACTABLE if every submodule of M is a homomorphic image
of M. Dually, a module M is called co-EPI-RETRACTABLE if it contains a copy of each of its …