3,914 research outputs found
Generalized Derivations with Commutativity and Anti-commutativity Conditions
Let R be a prime ring with 1, with char(R) ≠ 2; and let F : R → R be a generalized derivation. We determine when one of the following holds for all x,y ∈ R: (i) [F(x); F(y)] = 0; (ii) F(x)ΟF(y) = 0;
(iii) F(x) Ο F(y) = x Ο y .</p
Higher Derivatives and Finiteness in Rings
<p>Let n be a positive integer, R a prime ring, U a nonzero right ideal, and d a derivation on R. Under appropriate additional hypotheses, we prove that if d<sup>n</sup>(U) is finite, then either R is finite or d is nilpotent. We also provide an extension to semiprime rings.</p></p
Some conditions for finiteness and commutativity of rings
We present several new sufficient conditions for a ring to be finite; we give two conditions which for periodic rings R imply that R must be either finite or commutative; and we study commutativity in rings with only finitely many non-central subrings
A subsystem-independent generalization of entanglement
We introduce a generalization of entanglement based on the idea that
entanglement is relative to a distinguished subspace of observables rather than
a distinguished subsystem decomposition. A pure quantum state is entangled
relative to such a subspace if its expectations are a proper mixture of those
of other states. Many information-theoretic aspects of entanglement can be
extended to the general setting, suggesting new ways of measuring and
classifying entanglement in multipartite systems. By going beyond the
distinguishable-subsystem framework, generalized entanglement also provides
novel tools for probing quantum correlations in interacting many-body systems.Comment: 5 pages, 1 encapsulated color figure, REVTeX4 styl
On Prime Near-Rings with Generalized Derivation
Let N be a 3-prime 2-torsion-free zero-symmetric left near-ring with multiplicative center Z. We prove that if N admits a nonzero generalized derivation f such that f(N)⊆Z, then N is a commutative ring. We also discuss some related properties
On Generalized Periodic-Like Rings
Let R be a ring with center
Z, Jacobson radical J, and set N of all nilpotent
elements. Call R generalized periodic-like if for all x∈R∖(N∪J∪Z) there exist positive integers m, n of opposite parity for which xm−xn∈N∩Z. We identify some basic properties of such rings and prove some results on commutativity
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