Results 111 to 120 of about 2,393 (148)
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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 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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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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Mathematical Notes, 1995
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SEMIPRIME LEFT QUASI-MORPHIC RINGS
Journal of Algebra and Its Applications, 2013A ring R is called left quasi-morphic if {Ra ∣ a ∈ R} = {l(b)∣ b ∈ R} where l(b) denotes the left annihilator of b. In 2007 Camillo and Nicholson showed that if R is quasi-morphic (left and right) and satisfies the ACC on {Ra ∣ a ∈ R}, then R is an artinian principal ideal ring. This is a new characterization of these rings.
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Semiprime Rings with Hypercentral Derivations
Canadian Mathematical Bulletin, 1995AbstractLetRbe 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 ...
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Semiprime Goldie Generalised Matrix Rings
Canadian Mathematical Bulletin, 1995AbstractNecessary and sufficient conditions are given for a generalised matrix ring to be semiprime right Goldie.
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2016
In an earlier paper, the author developed a theory that in a semiprime torsion free ring, there is an essential direct sum of three completely unique and algebraically very different types of ideals, one of which is discrete and the others are continuous.
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In an earlier paper, the author developed a theory that in a semiprime torsion free ring, there is an essential direct sum of three completely unique and algebraically very different types of ideals, one of which is discrete and the others are continuous.
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On Jordan Structure in Semiprime Rings
Canadian Journal of Mathematics, 1976A remarkable theorem of Herstein [1, Theorem 2] of which we have made several uses states: If R is a semiprime ring of characteristic different from 2 and if U is both a Lie ideal and a subring of R then either U ⊂ Z (the centre of R) or U contains a nonzero ideal of R. In a recent paper [3] Herstein extends the above mentioned result significantly and
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1973
A ring S is a (classical) right quotient ring of a subring T if every regular element a ∈ T has an inverse in S and $$ S = \{ a{b^{ - 1}}|a,b \in T,b\;{\text{reular}}\} $$ Then T is an order in S (cf. 7.21). The following condition is necessary and sufficient for a ring T to possess a classical quotient ring: If a, b ∈ T, and if b is regular ...
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A ring S is a (classical) right quotient ring of a subring T if every regular element a ∈ T has an inverse in S and $$ S = \{ a{b^{ - 1}}|a,b \in T,b\;{\text{reular}}\} $$ Then T is an order in S (cf. 7.21). The following condition is necessary and sufficient for a ring T to possess a classical quotient ring: If a, b ∈ T, and if b is regular ...
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