ON THE (DE)HOMOGENIZATION OF SAGBI BASES FOR FREE ASSOCIATIVE ALGEBRAS

Abstract

This paper has been inspired by a note on (De) homogenization of Sagbi (Subalgebra Analog to Gr¨obner Bases for Ideals) Bases in a polynomial ring over a field K [4]. It intends to study the behavior of Sagbi Bases for Free Associative Algebras under non-central (De)homogenization technique with respect to an additional variable. This paper demonstrates how Sagbi Bases behave differently in Free Associative Algebras under the said technique compared to Sagbi Bases in polynomial rings. The explanation has been made by illustrating a few examples as well.