A ring R is called NLI (rings whose nilpotent elements form a Lie ideal) if for each a∈ N (R)
and b∈ R, ab− ba∈ N (R). Clearly, NI rings are NLI. In this note, many properties of NLI …

A purely extending module is a generalization of an extending module. In this paper, we
study several properties of purely extending modules and introduce the notion of purely …

Recall that a commutative ring R is said to be a normal ring if it is reduced and every two
distinct minimal prime ideals are comaximal. A finitely generated reduced R-module M is …

Let R be a ring, let I be an ideal of R, and let n be a fixed positive integer. We define and
study In-injective modules and In-flat modules. Moreover, we define and study left In …

Analogous to left pq-Baer property of a ring [GF Birkenmeier, JY Kim and JK Park, Principally
quasi-Baer rings, Comm. Algebra 29 (2001) 639–660], we say a right R-module M is endo …

Let R be a ring. The ring R is called right almost nil-injective, if for any a∈ N (R), there exists
a left ideal Xa of R such that lr (a)= Ra⊕ Xa. In this paper, we give some characterizations …

Extending the notion of a reduced ring, we call a right module M over a ring R a reduced
module if, for any m Є M and a€ R, ma= 0 implies mR Ma= 0. Various results of reduced …

In 1963, Utumi determined under what condition the maximal one-sided ring of quotients of
a ring is, in fact, two-sided. That is, he showed if a ring is nonsingular and cononsingular …

A left R-module M is said to be left singly injective if Ext R 1 (F/K, M)= 0 for any cyclic
submodule K of any finitely generated free left R-module F. In this paper, we study the notion …

Generalisations of von Neumann regular rings are considered through annihilators, purity
and certain special cyclic modules. Left self-injective regular, strongly regular and biregular …