Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By Deveno

Math Help - Proving isomorphism in lattices

  1. #1
    Member
    Joined
    Sep 2012
    From
    india
    Posts
    78

    Proving isomorphism in lattices

    The question is as follows:

    Let $f$ be a monomorphism from a lattice $L$ to a lattice $M$.Show that $L$ is isomorphic to a sublattice of $M$.

    My attempt:

    Since $f$ is a monomorphism from a lattice $L$ to a lattice $M$ therefore it will be a lattice homomorphism which is injective.
    Since, $f$ is injective therefore every element of $L$ will be mapped into a unique element in $f(L)$ and hence $M$,and also every element of $f(L)$ will have a unique preimage.

    Thus $f:L -> f(L)$ is bijective and hence a lattice homomorphism.
    Further $f(L)$ is a sublattice of $M$ and hence $L$ is isomorphic to a sublattice of $M$.

    Am I correct ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: Proving isomorphism in lattices

    Looks OK to me.
    Thanks from mrmaaza123
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Proving Isomorphism
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: June 4th 2013, 03:25 PM
  2. Proving isomorphism to Zn
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: November 20th 2011, 08:04 PM
  3. length of Lattices
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: October 5th 2011, 02:10 PM
  4. Pairs of lattices
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: September 29th 2011, 12:45 PM
  5. proving an isomorphism
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 19th 2009, 04:45 PM

Search Tags


/mathhelpforum @mathhelpforum