Let R be a ring such that every zero divisor x is expressible as a sum of a nilpotent element
and a potent element of R: x= a+ b, where a is nilpotent, b is potent, and ab= ba. We call …

Definition 1. A ring R is a non-D-ring provided there is a nonconstant polynomial f (x)€ R [x]
such that f (a)(EU (R)(the unit group of R) for every a€ R. The polynomial f (x) will be called a …

Let R be a ring with identity in which Z=* e (Z) for every right ideal Z and L= & (L) for every
left ideal L of R. Rings satisfying these conditions (or their variation) have been investigated …

Recall that a ring R is said to be regular in the sense of yon Neumann if for every a ε R, there
is an x ε R such that axa= a. If, in addition, R has an identity element 1, and there is such an …

The purpose of this paper is to study the structure of right ideals in right D-rings. In $1 we first
recall some results from 191. We introduce the relevant condition (MP). A right D-ring is said …

We introduce the concepts of left (right) zero-divisor rings, a class of rings without identity.
We call a ring R left (right) zero-divisor if rR (a)= 0 (lR (a)= 0) for every a∈ R, and call R …

A commutative ring S with identity element 1 is called an elementary divisor ring (resp.
Hermite ring) if for every matrix A over S there exist nonsingular matrices P, Q such that PAQ …

In this paper, we first show that if a ring R has exactly n two-sided zero divisors (zero
included) with then n≧ 2, is finite and its order is≧ n². Next we consider a ring R all of …

In [1], S. Endo proved that if J. is a normal left pp ring, then for any ae A, there exist a central
idempotent e and a left regular ele-ment d such that a= de. We prove that, in fact, normal pp …

The zero divisors of $ R/I $ for every ideal $ I $ of a Noetherian ring is a finite union of
primes. We take this property as a definition and study the class of rings so defined. Such …