Generator (mathematics) - List of Generators

List of Generators

A list of examples of generating sets follow.

• Generating set of an algebra: If A is a ring and B is an A-algebra, then S generates B if the only sub-A-algebra of B containing S is B itself.
• Generating set of a group: A set of group elements which are not contained in any subgroup of the group other than the entire group itself.
• Generating set of a ring: A subset S of a ring A generates A if the only subring of A containing S is A itself.
• Generating set of an ideal in a ring.
• A generator (category theory), in category theory, is an object that can be used to distinguish morphisms.
• In topology, a collection of sets which generate the topology is called a subbase.
• Generating set of a topological algebra: S is a generating set of a topological algebra A if the smallest closed subalgebra of A containing S is A itself.