Dependence relation

• if, then ;
• if, then there is a finite subset of, such that ;
• if is a subset of such that implies, then implies ;
• if but for some, then .

Examples

• Let be a vector space over a field The relation, defined by if is in the subspace spanned by, is a dependence relation. This is equivalent to the definition of linear dependence.
• Let be a field extension of Define by if is algebraic over Then is a dependence relation. This is equivalent to the definition of algebraic dependence.