Results 81 to 90 of about 474 (163)

Centralizing Mappings of Semiprime Rings

, 1987
Let R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism
W. S. Martindale, H. E. Bell
core   +1 more source

Derivations with Engel conditions in prime and semiprime rings [PDF]

, 2011
summary:Let $R$ be a prime ring, $I$ a nonzero ideal of $R$, $d$ a derivation of $R$ and $m, n$ fixed positive integers. (i) If $(d[x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. (ii) If $\mathop {\rm Char}R\neq 2$ and $[d(x),d(y)]_{m}
Huang, Shuliang
core   +1 more source

On functional identities involving n-derivations in rings [PDF]

Journal of Mahani Mathematical Research
In this paper, we explore various properties associated with the traces of permuting $n$-derivations satisfying certain functional identities that operate on a Lie ideal within prime and semiprime rings.
Vaishali Varshney, Shakir Ali, Naira Noor Rafiquee, Kok Wong   +3 more
doaj   +1 more source

A subdirect decomposition of semiprime rings and its application to maximal quotient rings

, 1974
Levy [2] has examined semiprime rings which are irredundant subdirect products of prime rings. In this note we look at the role of inessential prime ideals and see how every semiprime ring is a subdirect product of (i) a semiprime ring which is an ...
Louis Halle Rowen
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Derivations satisfying certain algebraic identities on Lie ideals [PDF]

Mathematica Moravica, 2019
Let d be a derivation of a semiprime ring R and L a nonzero Lie ideal of R. In this note, it is proved that every noncentral square-closed Lie ideal of R contains a nonzero ideal of R. Further, we use this result to characterize the conditions: d(xy) = d(
Sandhu Gurninder S., Kumar Deepak
doaj  

Soft Substructures in Quantales and Their Approximations Based on Soft Relations. [PDF]

Comput Intell Neurosci, 2022
Zhou H, Qurashi SM, Rehman MU, Shabir M, Kanwal RS, Khalil AM.   +5 more
europepmc   +1 more source

On derivations and semiprime ideal of rings

Let $R$ be an associative ring with a nonzero ideal $I$ and a semiprime ideal $T$ such that $T\subsetneq I.$ Let $K$ be a nonempty subset of $R$ and $d:R\to R$ be a derivation of $R$, if $[d(x),x]\in T$ for all $x\in K,$ then $d$ is said to be a $T$-commuting derivation on $K.$ We show that if some specific $T$-valued differential identities are ...
Sandhu, Gurninder Singh, Rehman, Nadeem Ur   +1 more
openaire   +2 more sources

Some remarks on topologically semiprime ideals [PDF]

Czechoslovak Mathematical Journal, 1984
This paper is concerned with topological generalizations of the intersection properties of prime ideals for algebraic semigroups. An ideal of S, a topological semigroup, is said to be topologically semiprime if it fails to intersect those compact monothetic sub- semigroups which it does not contain.
openaire   +2 more sources

Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings

International Journal of Mathematics and Mathematical Sciences, 2014
Let R be a 2-torsion free ring and let L be a noncentral Lie ideal of R, and let F:R→R and G:R→R be two generalized derivations of R. We will analyse the structure of R in the following cases: (a) R is prime and F(um)=G(un) for all u∈L and fixed ...
Vincenzo De Filippis, Nadeem UR Rehman, Abu Zaid Ansari   +2 more
doaj   +1 more source

Semiprime Rings with Hypercentral Derivations

, 1995
LetRbe a semiprime ring with a derivationd, λ a left ideal ofRandk, ntwo positive integers. Suppose that[d(xn),xn]k= 0 for allx∊ λ. Then [λ,R]d(R)= 0.
Tsiu-Kwen Lee
core   +1 more source