Multiplicative bases, Grobner bases, and right Grobner bases

In this paper, we study conditions on algebras with multiplicative bases so that there is a Grobner basis theory. We introduce right Grobner bases for a class of modules. We give an elimination theory and intersection theory for right submodules of projective modules in path algebras. Solutions to homogeneous systems of linear equations with coefficients in a quotient of a path algebra are studied via right Grobner basis theory. (C) 2000 Academic Press.