In linear algebra, a linear relation, or simply relation, between elements of a vector space or a module is a linear equation that has these elements as a solution. More precisely, if are elements of a (left) module M over a ring R (the case of a vector space over a field is a special case), a relation between is a sequence of elements of R such that The construction of higher order syzygy modules is generalized as the definition of free resolutions, which allows restating Hilbert's syzygy theorem as a polynomial ring in n indeterminates over a field has global homological dimension n.