Search

Abstract: Let R be a prime ring, C its extended centroid and (resp. Q) its left (resp. symmetric) Martindale quotient ring. Let δ be a σ-derivation of R, where σ is an automorphism of R. We show the equivalence of K-polynomials (resp. K-identities) of δ and cv-polynomials (resp. semi-invariant polynomials) in the Ore extension . We prove the existence of K-polynomials of δ in certain rather general family of maps. As applications, the following are proved among other things: Consider the expression , where and . [(1)] If then either R is a GPI-ring or for all . [(2)] If then either R is commutative or for all . [Copyright &y& Elsevier]

Abstract: Fourth root metrics are a special and important class of Finsler metrics, which have been applied to physics. In this paper, we study invariant fourth root Finsler metrics on the Grassmannian manifolds . By using the results from the theory of invariant polynomials of Lie groups, we obtain a complete classification of such metrics. Further, some invariant -th root Finsler metrics are also given. [ABSTRACT FROM AUTHOR]

Abstract: Alternating matrix polynomials, that is, polynomials whose coefficients alternate between symmetric and skew-symmetric matrices, generalize the notions of even and odd scalar polynomials. We investigate the Smith forms of alternating matrix polynomials, showing that each invariant factor is an even or odd scalar polynomial. Necessary and sufficient conditions are derived for a given Smith form to be that of an alternating matrix polynomial. These conditions allow a characterization of the possible Jordan structures of alternating matrix polynomials, and also lead to necessary and sufficient conditions for the existence of structure-preserving strong linearizations. Most of the results are applicable to singular as well as regular matrix polynomials. [Copyright &y& Elsevier]