example of a non-lattice homomorphism
Consider the Hasse diagram of the lattice of subgroups of the quaternion group
of order , . [The use of is only for a concrete realization of the lattice
.]
To establish an order-preserving map which is not a lattice isomorphism
one can simply “skip” , which we display graphically as:
Since containment is still preserved the map is order-preserving. However, the intersection (meet) of
and , which is , is not perserved under this
map. Thus it is not a lattice homomorphism.
Title | example of a non-lattice homomorphism![]() |
---|---|
Canonical name | ExampleOfANonlatticeHomomorphism |
Date of creation | 2013-03-22 16:58:31 |
Last modified on | 2013-03-22 16:58:31 |
Owner | Algeboy (12884) |
Last modified by | Algeboy (12884) |
Numerical id | 8 |
Author | Algeboy (12884) |
Entry type | Example |
Classification | msc 06B23 |