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GENERALIZED DERIVATIONS ON SEMIPRIME RINGS [PDF]
Bulletin of the Korean Mathematical Society, 2011 Let R be a prime ring, I a nonzero ideal of R and n a fixed positive integer. If R admits a generalized derivation F associated with a derivation d such that c for all x, . Then either R is commutative or n = 1, d = 0 and F is the identity map on R.
DE FILIPPIS, Vincenzo, S. Huang
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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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On Rings of Weak Global Dimension at Most One
Mathematics, 2021 A ring R is of weak global dimension at most one if all submodules of flat R-modules are flat. A ring R is said to be arithmetical (resp., right distributive or left distributive) if the lattice of two-sided ideals (resp., right ideals or left ideals) of
Askar Tuganbaev
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Jordan derivations on semiprime rings [PDF]
Proceedings of the American Mathematical Society, 1988 I. N. Herstein has proved that any Jordan derivation on a 2 2 -torsion free prime ring is a derivation.
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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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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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An Algebraic Structure of Type‐2 Soft Sets: Type‐(1,2) Soft Groups
Journal of Mathematics, Volume 2026, Issue 1, 2026.Recently, many researchers have been studying the algebraic structures of soft sets such as soft semigroups, soft groups, soft rings, etc., and they have obtained some properties of these structures by considering the properties of classical algebraic structures. However, the algebraic structures of Type‐2 soft sets are still in their infancy.
Fouzia Musbah Farag Abdualhamid +2 more
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Semiprime ideals in general lattices [PDF]
, 1989 The ring-theoretical concept of semiprime ideal is appropriately defined for lattices. We prove that an ideal I of a lattice L is semiprime iff I is the kernel of some homomorphisms of L onto a distributive lattice with zero. As a corollary we generalize
Rav, Yehuda
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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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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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