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Commutativity of rings with constraints on commutators
Results in Mathematics, 1985Let 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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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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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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Commutativity of rings with constraints on commutators
2000This 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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Canadian Journal of Mathematics, 1960
Let A, B, and X be n-square matrices over an algebraically closed field F of characteristic 0. Let [A, B] = AB — BA and set (A, B) = [A, [A, B]]. Recently several proofs (1; 3; 5) of the following result have appeared: if det (AB) ≠ 0 and (A,B) = 0 then A-1B-1AB - I is nilpotent.
Marcus, Marvin, Khan, Nisar A.
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Let A, B, and X be n-square matrices over an algebraically closed field F of characteristic 0. Let [A, B] = AB — BA and set (A, B) = [A, [A, B]]. Recently several proofs (1; 3; 5) of the following result have appeared: if det (AB) ≠ 0 and (A,B) = 0 then A-1B-1AB - I is nilpotent.
Marcus, Marvin, Khan, Nisar A.
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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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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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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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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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18th Annual Symposium on Foundations of Computer Science (sfcs 1977), 1977
In this paper we show that the computation of the determinant requires an exponential number of multiplications if the commutativity of indeterminates is not allowed. The determinant can be computed in polynomial time with the commutation of indeterminates.
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In this paper we show that the computation of the determinant requires an exponential number of multiplications if the commutativity of indeterminates is not allowed. The determinant can be computed in polynomial time with the commutation of indeterminates.
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The mapping class group is generated by two commutators
Journal of Algebra, 2021R Inanç Baykur, Mustafa Korkmaz
exaly
Writing commutators of commutators as products of cubes
Communications in Algebra, 2022Colin Ramsay
exaly
Commutativity, non-commutativity, and bilinearity
Information Processing Letters, 1976openaire +2 more sources