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### $\left(\sigma ,\tau \right)$-derivations on prime near rings

Archivum Mathematicum

There is an increasing body of evidence that prime near-rings with derivations have ring like behavior, indeed, there are several results (see for example [1], [2], [3], [4], [5] and [8]) asserting that the existence of a suitably-constrained derivation on a prime near-ring forces the near-ring to be a ring. It is our purpose to explore further this ring like behaviour. In this paper we generalize some of the results due to Bell and Mason [4] on near-rings admitting a special type of derivation...

### A canonical directly infinite ring

Czechoslovak Mathematical Journal

Let $ℕ$ be the set of nonnegative integers and $ℤ$ the ring of integers. Let $ℬ$ be the ring of $N×N$ matrices over $ℤ$ generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of $ℬ$ yields that the subrings generated by them coincide. This subring is the sum of the ideal $ℱ$ consisting of...

### A chain of Kurosh may have an arbitrary finite length

Czechoslovak Mathematical Journal

### A class of finite rings

Compositio Mathematica

### A combinatorial commutativity property for rings.

International Journal of Mathematics and Mathematical Sciences

### A commutativity theorem for associative rings

Archivum Mathematicum

Let $m>1,s\ge 1$ be fixed positive integers, and let $R$ be a ring with unity $1$ in which for every $x$ in $R$ there exist integers $p=p\left(x\right)\ge 0,q=q\left(x\right)\ge 0,n=n\left(x\right)\ge 0,r=r\left(x\right)\ge 0$ such that either ${x}^{p}\left[{x}^{n},y\right]{x}^{q}={x}^{r}\left[x,{y}^{m}\right]{y}^{s}$ or ${x}^{p}\left[{x}^{n},y\right]{x}^{q}={y}^{s}\left[x,{y}^{m}\right]{x}^{r}$ for all $y\in R$. In the present paper it is shown that $R$ is commutative if it satisfies the property $Q\left(m\right)$ (i.e. for all $x,y\in R,m\left[x,y\right]=0$ implies $\left[x,y\right]=0$).

### A commutativity theorem for left s-unital rings.

International Journal of Mathematics and Mathematical Sciences

### A commutativity-or-finiteness condition for rings.

International Journal of Mathematics and Mathematical Sciences

### A direct factor theorem for commutative group algebras

Commentationes Mathematicae Universitatis Carolinae

Suppose $F$ is a field of characteristic $p\ne 0$ and $H$ is a $p$-primary abelian $A$-group. It is shown that $H$ is a direct factor of the group of units of the group algebra $FH$.

### A general theory of Fountain-Gould quotient rings

Mathematica Slovaca

### A generalized Picard group for prime rings

Banach Center Publications

### A hypervaluation of a ring onto a totally ordered non-cancellative semigroup without zero divisors.

International Journal of Mathematics and Mathematical Sciences

### A note on centralizers.

International Journal of Mathematics and Mathematical Sciences

### A note on centralizers in $q$-deformed Heisenberg algebras.

AMA. Algebra Montpellier Announcements [electronic only]

### A note on commutativity of automorphisms.

International Journal of Mathematics and Mathematical Sciences

### A Note on Extensions of Bear and P.p.-rings

Publications de l'Institut Mathématique

### A note on isomorphic commutative group algebras over certain rings.

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

### A note on Jordan rings of quotients

Annales scientifiques de l'Université de Clermont. Mathématiques

### A note on rings which are multiplicatively generated by idempotents and nilpotents.

International Journal of Mathematics and Mathematical Sciences

### A note on rings with certain variable identities.

International Journal of Mathematics and Mathematical Sciences

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