A polynomial map preserving the finite basis property

The finite index basis property

We describe in this paper a connection between bifix codes, symbolic dynamical systems and free groups. This is in the spirit of the connection established previously for the symbolic systems corresponding to Sturmian words. We introduce a class of sets of factors of an infinite word with linear factor complexity containing Sturmian sets and regular interval exchange sets, namely the class of t...

The Finite Basis Extension Property and Graph Groups

Introduction: A theorem of Marshall Hall, Jr. [5] (cf. also [2], [4]) states that if B = {h1, ..., hk} is a free basis for a finitely generated subgroup H of a f.g. free group F , and if {x1, . . . , xn} is a finite subset of F −H, then B can be extended to a free basis for a f.g. subgroup H∗ of finite index in F such that {x1, . . . , xn} ⊂ F −H∗. A similar theorem holds for free abelian group...

The Polynomial Property (v)

Preserving zeros of a polynomial

We study non-linear surjective mappings on subsets of Mn(F), which preserve the zeros of some fixed polynomials in noncommuting variables. Mathematics subject classification (2000): 15A99, 16W99.

Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis

Bit-parallel finite field multiplication in F2m using polynomial basis can be realized in two steps: polynomial multiplication and reduction modulo the irreducible polynomial. In this article, we prove that the modular polynomial reduction can be done with (r − 1)(m − 1) bit additions, where r is the Hamming weight of the irreducible polynomial. We also show that a bit-parallel squaring operati...