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 …

We studied almost relative projective modules and almost relative injective modules in [3, 6,
7]. In this short note we define a new module, an almost projective (resp. almost injective) …

Let A be a class of some right R‐modules that is closed under isomorphisms, and let M be a
right R‐module. Then M is called A‐D3 if, whenever N and K are direct summands of M with …

A module is called locally pure-projective if every pure epimor-phism onto it is locally split.
We prove that every locally pure-projective module is a Mittag-Leffler module. We derive …

In this paper, we have introduced copure-direct-injective modules. A right R-module M is
said to be copure-direct-injective if every copure submodule of M isomorphic to a direct …

Let $ R $ be a ring and $ n $ a non-negative integer. In this paper, we first introduce the
concept of $ n $-super finitely copresented $ R $-modules and via these modules, we give a …

A module is called automorphism-invariant if it is invariant under any automorphism of its
injective hull. Dickson and Fuller have shown that if R is a finite-dimensional algebra over a …

Direct complements in a right R-module M are said to be almost unique if, whenever M= A⊕
B= A⊕ C, then (B+ C)/B≪ M/B (also (B+ C)/C≪ M/C, by symmetry). We will show that this …

ABSTRACT A right R-module M is called simple-direct-injective if, whenever, A and B are
simple submodules of M with A≅ B, and B⊆⊕ M, then A⊆⊕ M. Dually, M is called simple …

We introduce and investigate t-idempotent invariant modules. We call an endomorphism ψ
of M, at-idempotent endomorphism if ψ ̄: M/Z 2 (M)→ M/Z 2 (M) defined by ψ ̄ (m+ Z 2 …