Results 31 to 40 of about 123,101 (223)
Two elementary commutativity theorems for generalized boolean rings
International Journal of Mathematics and Mathematical Sciences, 1997 In this paper we prove that if R is a ring with 1 as an identity element in which xm−xn∈Z(R) for all x∈R and fixed relatively prime positive integers m and n, one of which is even, then R is commutative.
Vishnu Gupta
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Natural Inductive Theorems for Higher-Order Rewriting [PDF]
, 2011 The notion of inductive theorems is well-established in first-order term rewriting. In higher-order term rewriting, in contrast, it is not straightforward to extend this notion because of extensionality (Meinke, 1992).
Chiba, Yuki +2 more
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Commutativity of one sided s-unital rings through a Streb's result
International Journal of Mathematics and Mathematical Sciences, 1997 The main theorem proved in the present paper states as follows Let m, k, n and s be fixed non-negative integers such that k and n are not simultaneously equal to 1 and R be a left (resp right) s-unital ring satisfying [(xmyk)n−xsy,x]=0 (resp [(xmyk)n ...
Murtaza A. Quadri +2 more
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Symmetry‐Imposed Selection Rules for Excitations of Nontrivial Plasmonic Topologies
Advanced Science, EarlyView.A unified group‐theory selection rule governs the excitation of vectorial nearfield topologies across three plasmonic spin states. Derived from first principles, it predicts spin–orbit vortex splitting and multidimensional nested vortices, confirmed by phase‐resolved in situ measurements.
Jie Yang +14 more
wiley +1 more source
A Commutativity Theorem for Near-Rings [PDF]
Canadian Mathematical Bulletin, 1977 A ring or near-ring R is called periodic if for each xϵR, there exist distinct positive integers n, m for which xn = xm. A well-known theorem of Herstein states that a periodic ring is commutative if its nilpotent elements are central [5], and Ligh [6] has asked whether a similar result holds for distributively-generated (d-g) near-rings.
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A commutativity theorem for rings [PDF]
Bulletin of the Australian Mathematical Society, 1977 Let R be a ring with an identity and for each x, y in R, (xy)k = xkyk for three consecutive positive integers k. It is shown in this note that R is a commutative ring.
Ligh, Steve, Richoux, Anthony
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Commutativity Theorems in Groups with Power-like Maps
, 2019 There are several commutativity theorems in groups and rings which involve power maps f(x) = xn. The most famous example of this kind is Jacobson's theorem which asserts that any ring satisfying the identity xn = x is commutative.
Zhang, Yang, Padmanabhan, Ranganathan
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A Unifying Approach to Self‐Organizing Systems Interacting via Conservation Laws
Advanced Intelligent Discovery, EarlyView.The article develops a unified way to model and analyze self‐organizing systems whose interactions are constrained by conservation laws. It represents physical/biological/engineered networks as graphs and builds projection operators (from incidence/cycle structure) that enforce those constraints and decompose network variables into constrained versus ...
F. Barrows +7 more
wiley +1 more source
Rado's theorem for commutative rings
Journal of Combinatorial Theory, Series A, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vitaly Bergelson +3 more
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Compact Manifolds With Unbounded Nilpotent Fundamental Groups and Positive Ricci Curvature
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT It follows from the work of Kapovitch and Wilking that a closed manifold with nonnegative Ricci curvature has a uniformly almost nilpotent fundamental group. Leftover questions and conjectures, have asked if in this context the fundamental group is actually uniformly almost abelian. The main goal of this work is to construct examples (Mk9,gk)$(
Elia Bruè, Aaron Naber, Daniele Semola
wiley +1 more source