Results 41 to 50 of about 179 (118)
On Prime and Semiprime Rings with Symmetric Generalized Biderivations
Al-Mustansiriyah Journal of Science, 2017 The propose of this paper is to present some results concerning the symmetric generalized Biderivations when their traces satisfies some certain conditions on an ideal of prime and semiprime rings.
Auday H. Mahmood +1 more
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Prime Ideal, Semiprime Ideal, and Radical of an Ideal of an L-Subring
Fuzzy Information and Engineering, 2023 In this paper, we develop a systematic theory for the ideals of an L-ring L(μ, R). We introduce the concepts of a prime ideal, a semiprime ideal, and the radical of an ideal in an L-ring. The notion of a maximal ideal has been introduced and discussed in
Anand Swaroop Prajapati +2 more
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Additivity and Central Behavior of CE‐Generalized Homoderivations in Associative Rings
Journal of Mathematics, Volume 2026, Issue 1, 2026.This study examines the commutativity of a ring R endowed with a special class of mappings termed centrally extended generalized homoderivations. These mappings serve as an extension of several existing concepts, including homoderivations, generalized homoderivations, and left centralizers.
Hicham Saber +6 more
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Journal of Mathematics, Volume 2026, Issue 1, 2026.In this study, we investigate the behavior of semiprime ideals that satisfy certain algebraic identities using multiplicative (generalized) derivations. In addition, examples are provided to show that the limits imposed on the hypotheses of the different theorems are not superfluous.
Amal S. Alali +5 more
wiley +1 more source
Dependent Elements of Derivations on Semiprime Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2009 We characterize dependent elements of a commuting derivation d on a semiprime ring R and investigate a decomposition of R using dependent elements of d. We show that there exist ideals U and V of R such that U ⊕ V is an essential ideal of R, U∩V = {0}, d = 0 on U, d(V)⊆V, and d acts freely on V.
Faisal Ali, Muhammad Anwar Chaudhry
openaire +3 more sources
On Maps of Period 2 on Prime and Semiprime Rings
International Journal of Mathematics and Mathematical Sciences, 2014 A map f of the ring R into itself is of period 2 if f2x=x for all x∈R; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized ...
H. E. Bell, M. N. Daif
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Mathematica BohemicaWe study McCoy's theorem to the skew Hurwitz series ring $({\rm HR}, \omega)$ for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings.
Rajendra Kumar Sharma, Amit B. Singh
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Fully noncentral Lie ideals and invariant additive subgroups in rings
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic ≠2$\ne 2$ where every additive commutator is a sum of
Eusebio Gardella +2 more
wiley +1 more source
Generalized Derivations in Semiprime Gamma Rings [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 LetMbe a 2-torsion-free semiprimeΓ-ring satisfying the conditionaαbβc=aβbαcfor alla,b,c∈M, α,β∈Γ, and letD:M→Mbe an additive mapping such thatD(xαx)=D(x)αx+xαd(x)for allx∈M, α∈Γand for some derivationdofM. We prove thatDis a generalized derivation.
Kalyan Kumar Dey +2 more
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Prime Graphs of Polynomials and Power Series Over Noncommutative Rings
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.The prime graph PG(R) of a ring R is a graph whose vertex set consists of all elements of R. Two elements x, y ∈ R are adjacent in the graph if and only if xRy = 0 or yRx = 0. An element a ∈ R is called a strong zero divisor in R if 〈a〉〈b〉 = 0 or 〈b〉〈a〉 = 0 for some nonzero element b ∈ R. The set of all strong zero divisors is denoted by S(R).
Walaa Obaidallah Alqarafi +3 more
wiley +1 more source