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.

Read more about this topic:  Generator (mathematics)

Famous quotes containing the words list of and/or list:

    My list of things I never pictured myself saying when I pictured myself as a parent has grown over the years.
    Polly Berrien Berends (20th century)

    I made a list of things I have
    to remember and a list
    of things I want to forget,
    but I see they are the same list.
    Linda Pastan (b. 1932)