It is well known that a commutative ring R is complemented (that is, given a∈ R there exists
b∈ R such that ab= 0 and a+ b is a regular element) if and only if the total ring of quotients of …

In 1950 in volume 1 of Proc. Amer. Math. Soc., B. Brown and N. McCoy showed that every
(not necessarily commutative) ring $ R $ has an ideal $\frak M (R) $ consisting of elements …

From the original PREFACE: The rings of quotients recently introduced by Johnson and
Utumi are applied to the ring $ C (X) $ of all continuous real-valued functions on a …

In this paper we study algebraic closures for commutative semiprime rings. The main
interest, however, is with rings which are regular in the sense of von Neumann. These play …

All rings considered in this paper are commutative with unity. A ring R is called a PF-ring if
every principal ideal a R is a flat R-module. A ring R is called a PP-ring if every principal …

Full article: A CHARACTERIZATION OF UNIT REGULAR RINGS Skip to Main Content Taylor
and Francis Online homepage Taylor and Francis Online homepage Log in | Register Cart …

In this paper we define a generalized ring of quotients for an arbitrary associative ring and
find necessary and sufficient conditions for its existence. We investigate the relations …

All rings considered in this survey are commutative with identity. Let A be a subring of a ring
B (with the same 1) and let n⩽ 1 be an integer. We say that A is n-root closed in B if bn ϵ A …

In this manuscript, we transport the classical Operator Theory on complex Banach spaces to
normed modules over absolutely valued rings. In some cases, we are able to extend …

In this paper we show that a ring (not necessarily commutative) with identity element and
without nonzero nilpotent elements is a von Neumann regular ring if every completely prime …