Results 1 to 10 of about 381 (106)
Rank of elements of general rings in connection with unit-regularity [PDF]
Journal of Pure and Applied Algebra, 224 (2020), 106211, 2018 We define the rank of elements of general unital rings, discuss its properties and give several examples to support the definition. In semiprime rings we give a characterization of rank in terms of invertible elements. As an application we prove that every element in the socle of a unital semiprime ring is unit-regular.
Stopar, Nik
arxiv +3 more sources
An algebraic approach to Wigner's unitary-antiunitary theorem [PDF]
arXiv, 1998 We present an operator algebraic approach to Wigner's unitary-antiunitary theorem using some classical results from ring theory. To show how effective this approach is, we prove a generalization of this celebrated theorem for Hilbert modules over matrix algebras. We also present a Wigner-type result for maps on prime C*-algebras.
Dedicated To Réka Anna, Lajos Moln Ár
arxiv +5 more sources
Multiplicative generalized derivations on Lie ideals in semiprime rings II [PDF]
, 2017 Let R be a semiprime ring and L is a Lie ideal of R such that L 6 Z.R/. A map F WR!R is called a multiplicative generalized derivation if there exists a map d WR!R such that F.xy/D F.x/yCxd.y/; for all x;y 2 R: In the present paper, we shall prove that d
E. Koç, Ö. Gölbasi
semanticscholar +2 more sources
Skew $N$-Derivations on Semiprime Rings [PDF]
arXiv, 2012 For a ring $R$ with an automorphism $\sigma$, an $n$-additive mapping $\Delta:R\times R\times... \times R \rightarrow R$ is called a skew $n$-derivation with respect to $\sigma$ if it is always a $\sigma$-derivation of $R$ for each argument. Namely, it is always a $\sigma$-derivation of $R$ for the argument being left once $n-1$ arguments are fixed by $
Wei Zhang +5 more
arxiv +4 more sources
Some commutativity criteria involving endomorphism conditions on prime ideals
Hacettepe Journal of Mathematics and Statistics, 2022 In this paper we initiate a new approach consisting to characterize the commutativity of a quotient ring R/P by endomorphisms of R satisfying some algebraic identities involving the prime ideal P.
L. Oukhtite
semanticscholar +1 more source
CLASSIFICATION OF SOME SPECIAL GENERALIZED DERIVATIONS
International Electronic Journal of Algebra, 2021 The purpose of the present paper is to classify generalized derivations satisfying more specific algebraic identities in a prime ring with involution of the second kind.
M. A. Idrissi, L. Oukhtite
semanticscholar +1 more source
On The Identity d(x) = λx + ζ(x)
Journal of Al-Rafidain University College For Sciences ( Print ISSN: 1681-6870 ,Online ISSN: 2790-2293 ), 2021 The main purpose of this paper is to study and investigate some results concerning generalized derivation D on semiprime ring R, where d a derivation on R and R has a cancellation property with identity.
M. Atteya, D. Resan
semanticscholar +1 more source
Functional equations related to higher derivations in semiprime rings
Open Mathematics, 2021 We investigate the additivity and multiplicativity of centrally extended higher derivations and show that every centrally extended higher derivation of a semiprime ring with no nonzero central ideals is a higher derivation.
Ezzat O. H.
doaj +1 more source
Left Annihilator of Identities with Generalized Derivations in Prime and Semiprime Rings
Discussiones Mathematicae - General Algebra and Applications, 2021 Let R be a noncommutative prime ring of char (R) ≠ 2, F a generalized derivation of R associated to the derivation d of R and I a nonzero ideal of R. Let S ⊆ R.
Rahaman Md Hamidur
doaj +1 more source
On multiplicative centrally-extended maps on semi-prime rings
Journal of Taibah University for Science, 2022 In this paper, we show that for semi-prime rings of two-torsion free and 6-centrally torsion free, given a multiplicative centrally-extended derivation δ and a multiplicative centrally-extended epimorphism ϕ we can find a central ideal K and maps ...
M. S. Tammam EL-Sayiad, A. Ageeb
doaj +1 more source