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On semiprime Noetherian PI-rings [PDF]
Mathematical Journal of Okayama University, 2000 Let \(R\) be a semiprime Noetherian PI-ring, and let \(Q\) be its semisimple Artinian classical quotient ring. The author establishes the equivalence of the following three statements. (1) The (classical) Krull dimension of \(R\) is \(\leq 1\); (2) If \(T\) is a ring with \(R\subseteq T\subseteq Q\), then \(T\) is Noetherian; (3) For central regular ...
Chiba, Katsuo
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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 ...
Francesco Catino
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Semiprime Rings with Hypercentral Derivations
Canadian Mathematical Bulletin, 1995 AbstractLetRbe a semiprime ring with a derivationd, λ a left ideal ofRandk, ntwo positive integers. Suppose that[d(xn),xn]k= 0 for allx∊ λ. Then [λ,R]d(R)= 0. That is, there exists a central idempotente∊U, the left Utumi quotient ring ofR, such thatdvanishes identically oneUand λ(l —e) is central in (1 —e ...
Tsiu-Kwen Lee
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On Derivations in Semiprime Rings
Algebras and Representation Theory, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali, Shakir, Huang, Shuliang
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On τ-centralizers of semiprime rings
Siberian Mathematical Journal, 2007Summary: Let \(R\) be a semiprime 2-torsion free ring, and let \(\tau\) be an endomorphism of \(R\). Under some conditions we prove that a left Jordan \(\tau\)-centralizer of \(R\) is a left \(\tau\)-centralizer of \(R\). Under the same conditions we also prove that a Jordan \(\tau\)-centralizer of \(R\) is a \(\tau\)-centralizer of \(R\).
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Semiprime Rings with Nilpotent Derivatives
Canadian Mathematical Bulletin, 1981There has been a great deal of work recently concerning the relationship between the commutativity of a ring JR and the existence of certain specified derivations of R. Bell, Herstein, Procesei, Schacher, Ligh, Martindale, Putcha, Wilson, and Yaqub [1, 2, 6, 8, 9, 10, 11, 12, 14] have studied conditions on commutators which imply the commutativity of ...
Chung, L. O., Luh, Jiang
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Centralizing Mappings of Semiprime Rings
Canadian Mathematical Bulletin, 1987AbstractLet R be a ring with center Z, and S a nonempty subset of R. A mapping F from R to R is called centralizing on S if [x, F(x)] ∊ Z for all x ∊ S. We show that a semiprime ring R must have a nontrivial central ideal if it admits an appropriate endomorphism or derivation which is centralizing on some nontrivial one-sided ideal.
Bell, H. E., Martindale, W. S. III
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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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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 ...
Aydin, Neset +2 more
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THE SEMIPRIMENESS OF SEMIGROUP RINGS
JP Journal of Algebra, Number Theory and Applications, 2021Hirano, Yasuyuki +2 more
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