which allows restating Hilbert's syzygy theorem as a polynomial ring in indeterminates over a field has global homological dimension .

If and are two elements of the commutative ring , then is a relation that is said trivial. The module of trivial relations of an ideal is the submodule of the first syzygy module of the ideal that is generated by the trivial relations between the elements of a generating set of an ideal. The concept of trivial