Algebraic structures
Category. group
B. Ring
C. Body
D. Mortgage
A distributive lattice is called complementary, if it contains two elements n and e, apply to:
A distributive and complementary lattice is called a Boolean lattice or Boolean algebra.
E. Mapping of sets with algebraic structure
1. homomorphism
A mapping A of a set M with an algebraic structure onto a set M’ with an algebraic structure is called homomorphism, if
(1) The link(in) in M clearly the (the) connections) in M’ assigned;
(2) the mapping of the result of the link(in) in M of two elements of M equal to the result of the associated operation(in) in M’ of the images of the two elements.
If e.g. der Verknüpfung ∗ in M die Verknüpfung º in M’ assigned, so for x,y ∈ M
Category (x ∗ y) = A(x) A(y)
The algebraic structures are then called homomorphic.
2. isomorphism
A homomorphism is called an isomorphism, if the map A is bijective. The algebraic structures are then called isomorphic.