On the Theory of Graded Structures
It is well known that various notions of distinguished bases of ideals, such as standard and Grobner bases, and algorithms for constructing them, play a central role in solving algorithmic problems in polynomial ideal theory and related algebraic theories. In this paper a new structural algebraic framework is given for the concept and the construction of the so-called generalised standard bases. Although the spirit of this paper is more structural than algorithmic, the general results achieved should also help to shape and direct future research in the algorithmic aspects of commutative algebra.