Results 241 to 250 of about 12,398 (276)

Skew-commuting and commuting mappings in rings

aequationes mathematicae, 2002
Let \(R\) be a ring with center \(Z\), and \(S\) a nonempty subset of \(R\); and let \(n\) be a fixed positive integer. A mapping \(f\colon R\to R\) is called \(n\)-commuting (resp. \(n\)-centralizing) on \(S\) if \([x^n,f(x)]=0\) (resp. \([x^n,f(x)]\in Z\)) for all \(x\in S\). Similarly, \(f\) is \(n\)-skew-commuting (resp. \(n\)-skew-centralizing) on
Park, Kyoo-Hong, Jung, Yong-Soo
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On commuting mappings

Mathematical Notes, 2009
The cardinality of the centralizer of an element in infinite symmetric semigroups is studied.
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Commuting Maps of Triangular Algebras

Journal of the London Mathematical Society, 2001
We investigate commuting maps on a class of algebras called triangular algebras. In particular, we give sufficient conditions such that every commuting map \(L\) on such an algebra is of the form \(L(a)=ax+h(a)\), where \(x\) lies in the center of the algebra and \(h\) is a linear map from the algebra to its center.
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Commutativity Preserving Maps of Factors

Canadian Journal of Mathematics, 1988
By 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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$n$-commuting maps on prime rings

Publicationes Mathematicae Debrecen, 2004
Summary: We prove a result concerning additive \(n\)-commuting maps on prime rings and then apply it to \(n\)-commuting linear generalized differential polynomials.
Lee, T.-K., Liu, K.-S., Shiue, W.-K.
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On surjective linear maps preserving commutativity

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2004
We 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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Additive mappings preserving commutativity

Linear and Multilinear Algebra, 1997
The general form of additive surjective mappings on Mn which preserve commutativity in both directions is given.
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Commuting dual billiard maps

Geometriae Dedicata, 1994
The dual billiard map \(T\) is a map of the exterior \(E(c)\) of a smooth strictly convex closed curve \(c\) in the Euclidean (or, actually: affine) plane into itself, which is defined as follows: given a point \(x\in E(c)\), draw the right (from the view-point of \(x\)) tangent line to \(c\) through it and reflect \(x\) in the point of tangency to ...
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Images of commutator MAPS

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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Skew-commuting and Commuting Mappings in Rings with Left Identity

Results in Mathematics, 2004
Let \(R\) be a ring with left identity \(e\), and let \(H\) be an additive subgroup of \(R\) containing \(e\). Let \(F\colon R^n\to R\) be an \(n\)-additive map with trace \(f\). The principal theorems, all rather technical in their statements, assert that if \(R\) has appropriate restrictions on torsion and appropriate polynomials involving \(f(x ...
Sharma, R. K., Dhara, Basudeb
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