Canonical subalgebra bases in non-commutative polynomial rings
Canonical bases, also called SAGBI bases, for subalgebras of the non-commutative polynomial ring are investigated. The process of subalgebra reduction is defined. Methods, including generalizations of the standard Gröbner bases techniques, are developed for the test whether bases are canonical, and for the completion procedure of constructing canonical bases. The special case of homogeneous subalg