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Commutativity of rings with constraints on commutators

2000
This paper studies commutativity of rings \(R\) satisfying polynomial identities of the form\break \(x^t[x^n,y]y^r=[x,y^m]y^s\) and three similar forms, where \(n,m,r,s,t\) are suitably-chosen nonnegative integers. Whether the theorems are correct as stated is not clear, but for some \((n,m,r,s,t)\) the proofs given do not work.
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Commutativity of rings with constraints on commutators

Results in Mathematics, 1985
Let F denote a commutative ring, \(F\) the corresponding ring of polynomials in two non-commuting indeterminates, and F[X,Y] the ring of polynomials in two commuting indeterminates. A polynomial \(f(X,Y)\in F\) is called admissible if each of its monomials has length at least 3 and f(X,Y) has trivial image under the natural F-algebra map from \(F\) to ...
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On Commutative Squares

Canadian Journal of Mathematics, 1963
The following elementary facts about certain commutative diagrams, called "squares," are stated and proved in terms of abelian groups and their homomorphisms. However, they are valid for arbitrary abelian categories and can be proved also for them. This does not need to be shown, since every abelian category can be embedded into the category of abelian
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Commutators of operators

American Journal of Mathematics, 1952
A mathematical formulation of the famous Heisenberg uncertainty principle is that a certain pair of linear transformations P and Q satisfies, after suitable normalizations, the equation PQ - QP = 1. It is easy enough to produce a concrete example of this behavior; consider L2(-∞, +∞) and let P and Q be the differentiation transformation and the ...
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Commutative Involutions

The Mathematical Gazette, 1947
We prove some theorems on commutative involutions in a “real” projective geometry in which cobasal homographie ranges may have 0, 1 or 2 self-corresponding points (and therefore a conic and a general line in its plane have 0, 1 or 2 points of intersection).
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Sobolev regularity for commutators of the fractional maximal functions

Banach Journal of Mathematical Analysis, 2020
Feng Liu, Shuai Xi
semanticscholar   +1 more source

Sharp commutator estimates via harmonic extensions

Nonlinear Analysis: Theory, Methods & Applications, 2020
Armin Schikorra
exaly  

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