Noncommutative Grobner basis, Hilbert series, Anick's resolution and BERGMAN under MS-DOS

The definition and main results connected with Gröbner basis, Hilbert series and Anick's resolution are formulated. The method of the infinity behavior prediction of Gröbner basis in noncommu-tative case is presented. The extensions of BERGMAN package for IBM PC compatible computers are described. Let A =< X|R > be a finitely presented associative algebra over field K. Here are the main examples of algebras that will help us to illustrate some following definitions (later we will refer to them as main examples).