On the noetherianity of some associative finitely presented algebras

AbstractWe consider finitely generated associative algebras over a fixed field K of arbitrary characteristic. For such an algebra A we impose some structural restrictions (we call A strictly ordered). We are interested in the implication of strict order on A for its noetherian properties. In particular, we prove that if A is a graded standard finitely presented strictly ordered algebra, then A is left noetherian if and only if it is almost commutative. In this case A has polynomial growth