An Algorithm for Constructing Gröbner and Free Schreier Bases in Free Group Algebras

GrÖbner-shirshov Bases for Free Inverse Semigroups

A new construction for free inverse semigroups was obtained by Poliakova and Schein in 2005. Based on their result, we find Gröbner-Shirshov bases for free inverse semigroups with respect to the deg-lex order of words. In particular, we give the (unique and shortest) normal forms in the classes of equivalent words of a free inverse semigroup together with the Gröbner-Shirshov algorithm to trans...

An Algorithm for Free Algebras

We present an algorithm for constructing the free algebra over a given finite partial algebra in the variety determined by a finite list of equations. The algorithm succeeds whenever the desired free algebra

Hall and Gröbner bases and rewriting in free Lie algebras (Extended Abstract)

Constructing Free Groups in Quaternion Algebras

In [4] it was shown for a suitable power n of a pair of units u, v of the quaternions algebras over the ring of integers of imaginary rational extensions A = H(o Q √ −d ) that the group generated by u, v is a free group in the unit group of A when d ≡ 7 (mod 8) is a positive square free integer. We extend this result for any imaginary rational extension and show that the group generated by u, v...

GröBner-Shirshov Bases and Embeddings of Algebras

In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...