Noncommutative Grr Obner Bases. a Computational and Theoretical Tool
نویسنده
چکیده
Overview These notes consists of ve lectures. Each lecture covers the material that I will present with fuller details and exercises. I have also included some material in appendices which the reader might nd interesting but which I will not have time to cover in my lectures. Lecture 1 introduces both linear Grr obner bases and Grr obner bases for algebras. Lecture 2 surveys some of the basis algorithms of Grr obner basis theory. These include the Division Algorithm, and the Termination Theorem (Bergman's Diamond Lemma). Lecture 3 presents the noncommutative version of Buchberger's algorithm, universal Grr obner bases and considers the special case of nite dimensional algebras. Lecture 4 applies the theory of Grr obner bases to the study of modules. Pro-jective presentations and resolutions are considered. A method of constructing projective resolutions of nite dimensional modules is given. Lecture 5 considers further theoretical applications. The study of Koszul algebras via Grr obner bases in presented.
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