Identities for a parametric Weyl algebra over a ring

Linear Algebra over a Ring

Given an associative, not necessarily commutative, ring R with identity, a formal matrix calculus is introduced and developed for pairs of matrices over R. This calculus subsumes the theory of homogeneous systems of linear equations with coefficients in R. In the case when the ring R is a field, every pair is equivalent to a homogeneous system. Using the formal matrix calculus, two alternate pr...

A Necessary Condition for Weyl-Heisenberg Frames

On Skew Cyclic Codes over a Finite Ring

In this paper, we classify the skew cyclic codes over Fp + vF_p + v^2F_p, where p is a prime number and v^3 = v. Each skew cyclic code is a F_p+vF_p+v^2F_p-submodule of the (F_p+vF_p+v^2F_p)[x;alpha], where v^3 = v and alpha(v) = -v. Also, we give an explicit forms for the generator of these codes. Moreover, an algorithm of encoding and decoding for these codes is presented.

A Bound for the Nilpotency Class of a Lie Algebra

In the present paper, we prove that if L is a nilpotent Lie algebra whose proper subalge- bras are all nilpotent of class at most n, then the class of L is at most bnd=(d 1)c, where b c denotes the integral part and d is the minimal number of generators of L.

A Computer Algebra System for Nonassociative Identities 1

In recent years there has been an emergence of general purpose computer algebra systems such as Maple, Macsyma, Mathematica, and Reduce. These systems provide a wealth of facilities for performing symbolic algebraic computation. Many are capable of computing a Grobner bases of the ideal generated by a set of multivariate polynomials. Such systems work well at manipulating polynomials in variab...