Results 91 to 100 of about 475 (163)

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

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

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

Semiprime f-Rings That Are Subdirect Products of Valuation Domains [PDF]

, 1993
Recall that an f-ring is a lattice-ordered ring in which a Λ b = 0 implies a Λ bc = a Λ cb = 0 whenever c ≥ 0. In [BKW], an f-ring is defined to be a lattice-ordered ring which is a subdirect product of totally ordered rings.
Suzanne Larson, Larson, Suzanne, Henriksen, Melvin, Melvin Henriksen   +3 more
core   +1 more source

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

On nilpotent derivations of semiprime rings [PDF]

, 1992
In this paper we study nilpotent derivations of semiprime rings. An associative derivation d: R → R is an additive mapping on a ring R satisfying d(xy) = d(x) y + xd(y) for all x, y ϵ R.
Grzeszczuk, Piotr
core   +1 more source

A Generalization of Source of Semiprimeness

Journal of New Theory
This paper characterizes the semigroup ideal $\mathcal{L}_{R}^{n}(I)$ of a ring $R$, where $I$ is an ideal of $R$, defined by $\mathcal{L}_{R}^{0}(I)=I$ and $\mathcal{L}_{R}^{n}(I)=\{a\in R \mid aRa\subseteq \mathcal{L}_{R}^{n-1}(I)\}$, for all $n\in ...
Çetin Camcı, Rasie Mekera, Didem Karalarlıoğlu Camcı, Didem Yeşil   +3 more
doaj   +1 more source