Computing resolutions over associative algebras with ordered basis
Lawrence H. Smith, Jee Koh · 1998
An analogue of Grobner basis, S-polynomials, and the Buchberger algorithm is given for associative k-algebras with well ordered k-basis, making it possible to define a procedure for computing resolutions of modules similar to one currently known for polynomial rings. This theory is applied to quotients of polynomial rings suggesting an approach to computing in that situation that may be more efficient than the techniques currently practiced. Finally, to facilitate the feasibility of implementing a computer program capable of working with general associative algebras, an algorithmic characterization of total orders on free monoids is developed.