A basic problem in ring theory is to investigate when a ring can be represented as the full
ring of endomorphisms of a suitable module. This problem in its full generality is quite …

SUMMARY I. Kaplanskv, in [8], defines Baer rings as rings whose right (left) annihilators are
principal right (left) ideals generated by idempotents. KG Wolfson, in [12], investigates the …

REGULAR AND BAER RINGS 354 Page 1 proceedings of the american mathematical society
Volume 42, Number 2, February 1974 REGULAR AND BAER RINGS KM RANGASWAMY …

Introduction. Let K be the ring of all n by n matrices over a division ring R. Then each left
(right) ideal of K is a principal left (right) ideal generated by an idempotent element. We may …

A ring R of linear transformations of a vector space M over a division ring D is called
distinguished iff (1) the lattice J of all R-submodules of M is a distributive sublattice of the …

We clarify and algebraicize the construction of the'regular rings' of finite Baer $^\ast $ rings.
We first determine necessary and sufficient conditions of a finite Baer $^\ast $ ring so that its …

A Baer ring is a ring in which every right (and left) annihilator ideal is generated by an
idempotent. Generalizing quite naturally from the fact that the endomorphism ring of a vector …

Let MR be an arbitrary module. Then Mn is a JBaer module in case it satisfies Baer's
condition (the terminology of [2] will be used throughout), namely, in case for each [e HomR …

A ring R with unit element is a Baer ring if every left annihilator in R has the form Re, where e
is an idempotent element. KG Wolfson has proven [3, Corollary 15], that if R is a Priifer ring …

In this paper we will define an ideal (NE (R)) which provides a link between the set of
nilpotents and the set of idempotents of a ring R. In the first section various properties of (NE …