On recognisable properties of associative algebras (Q1115181)

An algebra, presented in the form \(A=K<X>/I\), where \(K\) is a field of arbitrary characteristic, \(I\) is an ideal and \(X\) is a finite set of indeterminates may have some recognizable properties. In this article one gets a description of properties that are recognizable as soon as \(I\) satisfies certain conditions (one can not solve the problem in general due to the unsolvable word problem in the class of finitely presented algebras), together with some (implemented) algorithms. The main classes of algebras that are examined consist of the standard (Gröbner) finitely presented algebras and monomial algebras.