Let R be a ring (not necessarily with identity) and let E denote the set of idempotents of R.
We prove that R is a direct sum of a J-ring (every element is a power of itself) and a nil ring if …

In [7], Corbas determined all finite rings in which the product of any two zero-divisors is zero,
and showed that they are of two types, one of characteristic p 2and the other of characteristic …

In this paper we present some basic results of the Universal Algebra of C∞− rings which
were nowhere to be found in the current literature. The outstanding book of I. Moerdijk and …

In his paper K. Asano [1, Theorem 3]'? proved that a commutative ring with the identity
element satisfying the ascending chain condition for ideals is a direct sum of a finite number …

Let R be an associative ring with a subring A such that for each xe R there exists an integer
n= n (x)> 1 with x" e A. In [16] Kaplansky proved that if R is semisimple and A is its center …

Let R be a semiprime ring (possibly without 1). The symmetric ring of quotients of R is
defined as the set of equivalence classes of essentially defined double centralizers (ƒ, g) on …

In this paper we consider analogues of Cohen's theorem. We introduce new notions of
almost prime left (right) submodule and dr-prime left (right) ideal, this allows us to extend …

The theory of special radicals was developed in the fundamental papers [3] and [4] of
ANDRUNAKmVI~. Though major contributions to the theory have subsequently been made …

This peper 142s motivated by one of Dinh van Huynh and. PF Sn? ith [a] in which some new
characterizations of semiprime Artinian rings and left Xoetherian rings were given by their c …

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 …