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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 , , , ,  and ) 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  on near-rings admitting a special type of derivation...

### 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 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 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

### A note on semiprime rings with derivation.

International Journal of Mathematics and Mathematical Sciences

### A remark concerning commutativity modulo radical in Banach algebras

Commentationes Mathematicae Universitatis Carolinae

### A result of commutativity of rings.

International Journal of Mathematics and Mathematical Sciences

### A theoreme on derivations in semiprime rings.

Collectanea Mathematica

### A weak periodicity condition for rings.

International Journal of Mathematics and Mathematical Sciences

### An iteration technique and commutativity of rings.

International Journal of Mathematics and Mathematical Sciences

### Anti-inverse rings.

Publications de l'Institut Mathématique. Nouvelle Série

### Centers in domains with quadratic growth

Open Mathematics

Let F be a field, and let R be a finitely-generated F-algebra, which is a domain with quadratic growth. It is shown that either the center of R is a finitely-generated F-algebra or R satisfies a polynomial identity (is PI) or else R is algebraic over F. Let r ∈ R be not algebraic over F and let C be the centralizer of r. It is shown that either the quotient ring of C is a finitely-generated division algebra of Gelfand-Kirillov dimension 1 or R is PI.

Semigroup forum

### Centralizers and Lie ideals

Rendiconti del Seminario Matematico della Università di Padova

### Centralizers on prime and semiprime rings

Commentationes Mathematicae Universitatis Carolinae

The purpose of this paper is to investigate identities satisfied by centralizers on prime and semiprime rings. We prove the following result: Let $R$ be a noncommutative prime ring of characteristic different from two and let $S$ and $T$ be left centralizers on $R$. Suppose that $\left[S\left(x\right),T\left(x\right)\right]S\left(x\right)+S\left(x\right)\left[S\left(x\right),T\left(x\right)\right]=0$ is fulfilled for all $x\in R$. If $S\ne 0$$\left(T...$

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