In this paper we study rings in which finitely generated flat modules are projective. First we
show that if the associated Lie ring of the ring R, is nilpotent, then cyclic flat left modules are …

In this paper, we introduce and study the pure-direct-projective modules, that is the modules
M every pure submodule A of which with M/A isomorphic to a direct summand of M is a direct …

In a recent paper by Wang and Ding, it was stated that any ring which is generalized
supplemented as a left module over itself is semiperfect. The purpose of this note is to show …

We introduce the class of “right almost V-rings” which is properly between the classes of
right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R …

ON A CLASS OF SEMIPERFECT RINGS Page 1 Journal of Algebra and Its Applications Vol.
12, No. 6 (2013) 1350009 (13 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219498813500096 …

A ring is called right SAP if every right simple module over it is absolutely pure. In this paper
we prove that every right SAP ring is semiprimitive and that the homomorphic image and the …

The structure of almost projective modules can be better understood in the case when the
following Condition (P) holds: The union of each countable pure chain of projective modules …

Abstract A module M is CS if every submodule of M is essential in a direct summand of M. In
this note we use the CS condition to provide conditions for semiperfect rings to be self …

Let R be a ring, and n and d fixed non-negative integers. An R-module M is called (n, d)-
injective if Ext d+ 1 R (P, M)= 0 for any n-presented R-module P. M is said to be (n, d) …

Introduction. The aim of this paper is to study conditions which reflect the projectivity of a
given finitely generated flat module over a commutative ring. The use of the invariant factors …