M. Harada defined an almost projective module in [8] and showed that semisimple rings,
serial rings, QF-rings and H-rings are well-characterized by the property of an almost …

A. Tozaki and the author defined almost relative projective modules in [5], and the author
has given a new concept of almost projective modules in [6]. On the other hand, we know …

In [6] an almost N-projective module is defined as a generalization of a N-projective module
to characterize the lifting property. This module is further studied in the succeeding papers …

In this paper we assume that every ring R is an associative ring with identity and R is two-
sided artinian. The author has defined almost projective modules and almost injective …

A well-known result of Osofsky [10, 11] states that a ring R is semisimple artinian iff every
cyclic R-module is injective. From this it follows that a right self-injective right hereditary ring …

A ring R is said to be left n-semihereditary, if every n-generated left ideal of R is projective. It
is shown that for a ring R, the following statements are equivalent:(1) R is left n …

We have given some characterizations of right Nakayama rings related to almost relative
projectives or almost relative injectives [12]. In this paper we shall study particularly the …

Let R be an artinian ring. We consider the following condition: if eR/A is/K/i?-projective (resp.
N-projective for an fl-module TV), then every submodule M'of eR/A is/K/i?-projective (resp …

Conditions for the endomorphism ring of a (finitely generated) projective module to be left
(semi) hereditary have been studied in several papers ([2],[7],[8]). In [2] and [8] it is shown …

Let R be an artinian ring. In [10], we have studied R on which the following condition holds:
for i?-modules M and N, if M is iV-projective, then Mf is always almost iV-projective for every …