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Affirmative answer to the Question of Leroy and Matczuk on injectivity of endomorphisms of semiprime left Noetherian rings with large images [PDF]
V. V. Bavula
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*-Differential Identities of Semiprime Rings with Involution
Journal of Algebra, 1996 openaire +2 more sources
Some Equations in Rings Involving Semiprime Ideals and Multiplicative Generalized Semiderivations
Ali Yahya Hummdi +3 more
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Symmetric Reverse $n$-Derivations on Ideals of Semiprime Rings
Shakir Ali +4 more
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On the Adjoint Group of Semiprime Rings
Communications in Algebra, 2006An associative ring R, not necessarily with a unity, is called semiprime if it has no nonzero nilpotent ideal. It is proved that in the adjoint group of a semiprime ring R every soluble-by-finite normal subgroup centralizes the Jacobson radical of R. In particular, if R is a semiprime ring with unity, then the same result holds for the multiplicative ...
CATINO, Francesco +2 more
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On Derivations in Semiprime Rings
Algebras and Representation Theory, 2011Let R be a ring, S a nonempty subset of R and d a derivation on R. A mapping \(f:R\longrightarrow R\) is called commuting on S if [f(x),x] = 0 for all x ∈ S. In this paper, our purpose is to produce commutativity results for rings and show that if R is a 2-torsion free semiprime ring and I a nonzero ideal of R, then a derivation d of R is commuting on ...
Huang Shuliang, Shakir Ali
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THE SOURCE OF SEMIPRIMENESS OF RINGS
2018Let R be an associative ring. We define a subset S-R of R as S-R = {a is an element of R vertical bar aRa = (0)} and call it the source of semiprimeness of R. We first examine some basic properties of the subset S-R in any ring R, and then define the notions such as R being a vertical bar S-R vertical bar-reduced ring, a vertical bar S-R vertical bar ...
Demir C., Aydin N., Camci D.K.
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Mathematical Notes, 1995
It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx n A=Ax n . We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive ...
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It is proved that a right distributive semiprime PI ringA is a left distributive ring and for each elementx ∈A there is a positive integern such thatx n A=Ax n . We describe both right distributive right Noetherian rings algebraic over the center of the ring and right distributive ...
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On Prime and Semiprime Rings with Derivations
Algebra Colloquium, 2006Let R be a ring and S a nonempty subset of R. A mapping f: R → R is called commuting on S if [f(x),x] = 0 for all x ∈ S. In this paper, firstly, we generalize the well-known result of Posner related to commuting derivations on prime rings. Secondly, we show that if R is a semiprime ring and I is a nonzero ideal of R, then a derivation d of R is ...
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