on magnus' freiheitssatz and free polynomial algebras

Free Algebras and the Freiheitssatz

We prove the Freiheitssatz for free associative algebras over any field. This extends the previous result of Marker-Limanov and immediately implies the Freiheitssatz for free restricted Lie algebras and free Lie algebras. We prove the Freiheitssatz for free Poisson algebras over a field of characteristic zero. This answers a question of MarkerLimanov and Umirbaev in the affirmative.

The Freiheitssatz and the Automorphisms of Free Right-symmetric Algebras

We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are free and automorphisms of two generated free right-symmetric algebras are tame. Mathematics Subject Classification (2000): Primary 17A36, 17A50; Secondary 1...

On free annotated algebras

On the maximal ideal space of extended polynomial and rational uniform algebras

Let K and X be compact plane sets such that K X. Let P(K)be the uniform closure of polynomials on K. Let R(K) be the closure of rationalfunctions K with poles o K. Dene P(X;K) and R(X;K) to be the uniformalgebras of functions in C(X) whose restriction to K belongs to P(K) and R(K),respectively. Let CZ(X;K) be the Banach algebra of functions f in C(X) suchthat fjK = 0. In this paper, we show th...

Polynomial algebras on classical Banach spaces

The classical Stone-Weierstrass theorem claims that the algebra of all real polynomials on a finite-dimensional real Banach space X is dense, in the topology of uniform convergence on bounded sets (we will always consider this topology, unless otherwise stated), in the space of continuous real functions on X. On the other hand ([12]), on every infinite-dimensional Banach space X there exists a ...

A Note on Solvable Polynomial Algebras

In terms of their defining relations, solvable polynomial algebras introduced by Kandri-Rody and Weispfenning [J. Symbolic Comput., 9(1990)] are characterized by employing Gröbner bases of ideals in free algebras, thereby solvable polynomial algebras are completely determinable and constructible in a computational way.