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Commutativity Preserving Maps of Factors
Canadian Journal of Mathematics, 1988By a von Neumann algebra M we mean a weakly closed, self-adjoint algebra of operators on a Hilbert space which contains I, the identity operator. A factor is a von Neumann algebra whose centre consists of scalar multiples of I.In all that follows ϕ:M → N will be a one to one, *-linear map from the von Neumann factor M onto the von Neumann algebra N ...
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Communications in Algebra, 1994
The commutator map θα: G → G associated with the element α of the group G is defined by θα(g) = g −1α−1gα for all g ∊ G. In this paper we prove that if the image θα is a subgroup of the finite group G, then θα(G) is soluble. (This in fact generalises the well-known result which states that all finite groups that admit a fixed-point-free automorphism ...
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The commutator map θα: G → G associated with the element α of the group G is defined by θα(g) = g −1α−1gα for all g ∊ G. In this paper we prove that if the image θα is a subgroup of the finite group G, then θα(G) is soluble. (This in fact generalises the well-known result which states that all finite groups that admit a fixed-point-free automorphism ...
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On surjective linear maps preserving commutativity
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004We describe surjective linear maps preserving commutativity from (symmetric elements of) any algebra (with involution) onto (symmetric elements of) a prime algebra (with involution) not satisfying polynomial identities of low degree. Bijective commutativity preservers on skew elements of centrally closed prime algebras with involution of the first kind
Beidar, K. I., Lin, Ying-Fen
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Commutative semifields from projection mappings
Designs, Codes and Cryptography, 2010Let \(q\) be a power of the odd prime \(p\), \(m\) an odd natural number, and let \(F\) be the field with \(q^{2m}\) elements. Sitting inside \(F\) are the fields \(F_q\), \(K\), \(L\), with \(q\), \(q^2\), \(q^m\) elements, respectively. For any map \(f: F\to F\) define the polarization \(x\ast y:=(f(x+y)-f(x)-f(y))/2\). Then \(f\) is called planar if
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Commuting Maps Lacking Commuting Extensions
The American Mathematical Monthly, 1967D. R. Anderson, D. C. Kay
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Commuting Analytic Maps: 11070
The American Mathematical Monthly, 2006Roberto Tauraso, Richard Stong
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Invariant approximations for commuting mappings in CAT(0) and hyperconvex spaces
Journal of Mathematical Analysis and Applications, 2008Naseer Shahzad, Jack Markin
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