Results 121 to 130 of about 852 (157)
Sums of Semiprime, Z, and D L-Ideals in a Class of F-Rings
, 1990 In this paper it is shown that there is a large class of f-rings in which the sum of any two semiprime i-ideals is semiprime. This result is used to give a class of commutative f-rings with identity element in which the sum of any two z-ideals which are ...
Larson, Suzanne
core
Sets of lengths in maximal orders in central simple algebras.
J Algebra, 2013 Smertnig D.
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A description of incidence rings of group automata
, 2008 Group automata occur in the Krohn-Rhodes Decomposition Theorem and have been extensively investigated in the literature. The incidence rings of group automata were introduced by the first author in analogy with group rings and incidence rings of graphs ...
Passman, D.S., Kelarev, Andrei
core
Centralizing Mappings of Semiprime Rings
Canadian Mathematical Bulletin, 1987 AbstractLet 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 semiprime Noetherian PI-rings
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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Left ideals and derivations in semiprime rings
Journal of Algebra, 2004 This paper obtains Posner's theorem for products of derivations on left ideals in semiprime rings, so describes when a product of derivations D and E of a semiprime ring R can act as a derivation on a left ideal L of R.
Charles Lanski
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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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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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