Structure of rings with certain conditions on zero divisors
H Abu-Khuzam, A Yaqub - International journal of mathematics …, 2006 - Wiley Online Library
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 …
and a potent element of R: x= a+ b, where a is nilpotent, b is potent, and ab= ba. We call …
A Note on Dedekind Non-D-Rings
KA Loper - The Rocky Mountain Journal of Mathematics, 1993 - JSTOR
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 …
such that f (a)(EU (R)(the unit group of R) for every a€ R. The polynomial f (x) will be called a …
[引用][C] On dual rings and their modules
CR Hajarnavis, NC Norton - Journal of Algebra, 1985 - Elsevier
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 …
left ideal L of R. Rings satisfying these conditions (or their variation) have been investigated …
On a class of regular rings that are elementary divisor rings
M Henriksen - 1973 - scholarship.claremont.edu
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 …
is an x ε R such that axa= a. If, in addition, R has an identity element 1, and there is such an …
On the ideal structure of right distributive rings
M Ferrero, G Törner - Communications in Algebra, 1993 - Taylor & Francis
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 …
recall some results from 191. We introduce the relevant condition (MP). A right D-ring is said …
[PDF][PDF] Rings in which every element is a left zero-divisor
Y Ren, Y Wang - J. Math. Res. Appl, 2013 - jmre.ijournals.cn
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 …
We call a ring R left (right) zero-divisor if rR (a)= 0 (lR (a)= 0) for every a∈ R, and call R …
Some remarks on elementary divisor rings II
M Henriksen - 1955 - scholarship.claremont.edu
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 …
Hermite ring) if for every matrix A over S there exist nonsingular matrices P, Q such that PAQ …
Some finiteness conditions for rings
Y Hirano - Chinese Journal of Mathematics, 1988 - JSTOR
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 …
included) with then n≧ 2, is finite and its order is≧ n². Next we consider a ring R all of …
ON VON NEUMANN REGULAR RINGS XI
RYUECHI MING, RYUSCHI MING - Bulletin mathématique de la Société des …, 1987 - JSTOR
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 …
idempotent e and a left regular ele-ment d such that a= de. We prove that, in fact, normal pp …
Zero divisors in Noetherian-like rings
EG Evans - Transactions of the American Mathematical Society, 1971 - ams.org
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 …
primes. We take this property as a definition and study the class of rings so defined. Such …