Mason introduced the reflexive property for ideals, and then this concept was generalized by
Kim and Baik, defining idempotent reflexive right ideals and rings. In this article, we …

The rings of this paper are assumed to have relations of orthogonality defined on them. Such
relations are uniquely determined by complete boolean algebras of ideals. Using the Stone …

We introduce the notions of the Baer and the quasi-Baer properties in a general module
theoretic setting. A module M is called (quasi-) Baer if the right annihilator of a (two-sided) …

We investigate Ore extensions of Baer rings and pp-rings. Let α be an endomorphism and δ
an α-derivation of a ring R. Assume that R is an α-rigid ring. Then (1) R is a Baer ring if and …

Jacobson said aa right ideal would be called bounded if it contained a non-zero ideal, and
Faith said a ring would be called strongly right bounded if every non-zero right ideal were …

A systematic exposition of Baer*-Rings, with emphasis on the ring-theoretic and lattice-
theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio …

A ring $ R $ with an automorphism $\sigma $ and a $\sigma $-derivation $\delta $ is called
$\delta $-quasi-Baer (resp., $\sigma $-invariant quasi-Baer) if the right annihilator of every …

Mackey and Ornstein proved that if R is a semi-simple ring then the ring of row and column
finite matrices over R (RCFMΓ (R)) is a Baer ring for any infinite set Γ. A ring with identity is a …

M. Harada (“Ring Theory, Proceedings of 1978 Antwerp Conference,” pp. 669–690, Dekker,
New York, 1979) studied the following two conditions:(*) Every non-small leftR-module …

A Baer ring is a ring in which every right (and left) annihilator ideal is generated by an
idempotent. If B is a Baer ring, then the set of principal right ideals of B which are generated …