Semisimple Module - Properties

Properties

  • If M is semisimple and N is a submodule, then N and M/N are also semisimple.
  • If each is a semisimple module, then so is .
  • A module M is finitely generated and semisimple if and only if it is Artinian and its radical is zero.

Read more about this topic:  Semisimple Module

Famous quotes containing the word properties:

    The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.
    John Locke (1632–1704)

    A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.
    Ralph Waldo Emerson (1803–1882)