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Journal of Algebra and Its ApplicationsFor a nonempty subset [Formula: see text] of a ring [Formula: see text], the ring [Formula: see text] is called [Formula: see text]-semiprime if, given [Formula: see text], [Formula: see text] implies [Formula: see text]. This provides a proper class of semiprime rings.
Grigore Călugăreanu +2 more
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Regular elements in semiprime rings [PDF]
Proceedings of the American Mathematical Society, 1968 In the proof of Goldie's theorem [1, Theorem 4.1], one of the crucial steps is to establish that every large right ideal contains a regular element [1, Theorem 3.9]. Recently, S. A. Amitsur told one of the authors he had proved, using the weaker conditions of the ACC on left and right annihilators, that every prime ring contains a left regular element ...
Johnson, R. E., Levy, L. S.
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Permuting Generalized f‐Triderivations on Lattices
Journal of Mathematics, Volume 2026, Issue 1, 2026.G. Szász initially proposed the idea of lattice derivation, and it has since been revived in the study of other problems in various branches of mathematics and applied sciences. The intention of the current research is to examine the structure of permuting generalized f‐triderivation linked with permuting f‐triderivation on lattice T,∧,∨ and to provide
Areej Almuhaimeed +3 more
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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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IDENTITIES WITH MULTIPLICATIVE GENERALIZED (α,α)-DERIVATIONS OF SEMIPRIME RINGS
Kragujevac Journal of MathematicsLet R be a semiprime ring and α be an automorphism of R. A mapping F : R → R (not necessarily additive) is called multiplicative generalized (α,α)-derivation if there exists a unique (α,α)-derivation d of R such that F(xy) = F(x)α(y) + α(x)d(y) for all x,
G. Sandhu, A. Ayran, Neşet Aydın
semanticscholar +1 more source
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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On semiprime rings of bounded index [PDF]
Proceedings of the American Mathematical Society, 1982 A ring R R is of bounded index (of nilpotency) if there is an integer
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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
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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
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