Let R be an associative ring with center Z(R) , I a nonzero ideal of and  be automorphism  of . An 3-additive mapping M:RxRxR is called symmetric left -3-centralizer if M(u1y,u2 ,u3)=M(u1,u2,u3)(y) holds for all  y, u1, u2, u3 In this paper we shall investigate the  commutativity prime rings admitting satisfying any one following conditions : (i)M([u ,y], u3)  [(u), (y)...

We compute matrix units for Brauer’s centralizer algebras and Hecke algebras of type A. This can be used to construct a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except S0(2n)) and their quantum deformations. The calculation is done by induction inspired by path models for special operator algebras. It is similar to the calculation of Young’...

For each of the classical Lie algebras g(n) = o(2n+ 1), sp(2n), o(2n) of type B, C, D we consider the centralizer of the subalgebra g(n−m) in the universal enveloping algebra U(g(n)). We show that the nth centralizer algebra can be naturally projected onto the (n− 1)th one, so that one can form the projective limit of the centralizer algebras as n → ∞ with m fixed. The main result of the paper ...

INTRODUCTION Femoral centralizers in total hip arthroplasty (THA) are designed to improve the neutral implant position and ensure a homogeneous cement mantle without implant-bone impingement. To date there are no data about the cement mantle configuration and implant position after malinsertion, as seen in mini-open approaches or adipose patients with a limited view. The present biomechanical s...

An extension L/K of skew fields is called a leftpolynomialextension with polynomial generator 0 if it has a left basis of the form 1, i3, ti’, , Bnm’ for some n. This notion of left polynomial extension is a generalisation of the notion of pseudo-linear extension, known from literature. In this paper we show that any polynomial which is the minimal polynomial over K of some element in an extens...

We study centralizers of elements in domains. We generalize a result of the author and Small [4], showing that if A is a finitely generated noetherian domain and a ∈ A is not algebraic over the extended centre of A then the centralizer of a has Gelfand-Kirillov dimension at most one less than the Gelfand-Kirillov dimension of A. In the case that A is a finitely generated noetherian domain of GK...

We survey the known results on two old open problems on commutation of languages. The first problem, raised by Conway in 1971, is asking if the centralizer of a rational language must be rational as well – the centralizer of a language is the largest set of words commuting with that language. The second problem, proposed by Ratoandromanana in 1989, is asking for a characterization of those lang...

We introduce the linear centralizer method for a passive adversary to extract the shared key in group-theory based key exchange protocols (KEPs). We apply this method to obtain a polynomial time cryptanalysis of the Commutator KEP, introduced by Anshel–Anshel–Goldfeld in 1999 and considered extensively ever since. We also apply this method to the Centralizer KEP, introduced by Shpilrain–Ushakov...