Definition (weakly distributive homomorphisms). A homomorphism μ : S → T between join-semilattices S and T is weakly distributive, if for all a, b in...

Then, for a homomorphism f : G → H, (f(u),f(v)) is an arc (directed edge) of H whenever (u,v) is an arc of G. There is an injective homomorphism from G to...

can be found in the article Distributivity (order theory). A morphism of distributive lattices is just a lattice homomorphism as given in the article on...

structure, too. In particular, a bounded-lattice homomorphism (usually called just "lattice homomorphism") f {\displaystyle f} between two bounded lattices...

between two Boolean algebras A and B is a homomorphism f : A → B with an inverse homomorphism, that is, a homomorphism g : B → A such that the composition g...

operations left distributivity and right distributivity are not equivalent, and require separate proofs. Given K-algebras A and B, a homomorphism of K-algebras...

like any homomorphism of mathematical objects, is just a mapping that preserves the structure of the objects. Another name for a homomorphism of R-modules...

kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism is a function...

and (T, ∨), a homomorphism of (join-) semilattices is a function f: S → T such that f(x ∨ y) = f(x) ∨ f(y). Hence f is just a homomorphism of the two semigroups...

dropped. A ring homomorphism f is said to be an isomorphism if there exists an inverse homomorphism to f (that is, a ring homomorphism that is an inverse...

following are equivalent: x is a distributive element; The map φ defined by φ(y) = x ∨ y is a lattice homomorphism from L to the upper closure ↑x = {...

bounded lattice homomorphism jx that maps all lower sets containing x to 1 and all other lower sets to 0. And, for any lattice homomorphism from J(P) to...

power p. The map x ↦ xp then defines a ring homomorphism R → R, which is called the Frobenius homomorphism. If R is an integral domain it is injective...

equivalence class. In fact, every homomorphism h determines a congruence relation via the kernel of the homomorphism, k e r h = { ( a , a ′ ) ∈ A 2 | h...

concerning the closure operations of homomorphism, subalgebra and product Birkhoff's representation theorem for distributive lattices Birkhoff's theorem (equational...

homomorphic image under a weakly distributive homomorphism (which is also easy), and (3) that there exists a distributive (∨,0)-semilattice of cardinality...

duality theory for distributive lattices provides three different (but closely related) representations of bounded distributive lattices via Priestley...

word, was coined), in a 1982 paper by Sergei Matveev (under the name distributive groupoids) and in a 1986 conference paper by Egbert Brieskorn (where...

Distributivity An operation ∗ {\displaystyle *} is distributive with respect to another operation + {\displaystyle +} if it is both left-distributive...

both left and right semimedial Left distributive If it satisfies the identity x • yz ≡ xy • xz Right distributive If it satisfies the identity yz • x...

homomorphisms between them. There exists a unique homomorphism from the two-element Boolean algebra 2 to every Boolean algebra, since homomorphisms must...

finite distributive lattices Fundamental theorem of Galois theory Fundamental theorem of geometric calculus Fundamental theorem on homomorphisms Fundamental...

all elements x of P and all subsets S of P, the following infinite distributivity law holds: x ∧ ⋁ s ∈ S s = ⋁ s ∈ S ( x ∧ s ) . {\displaystyle x\land...

function f: L→M between two complete lattices L and M is a complete homomorphism if f ( ⋀ A ) = ⋀ { f ( a ) ∣ a ∈ A } {\displaystyle f\left(\bigwedge...

correspondence between Boolean algebras and their Stone spaces, each homomorphism from a Boolean algebra A to a Boolean algebra B corresponds in a natural...

completely distributive lattice M and monotonic function f : C → M {\displaystyle f:C\rightarrow M} , there is a unique complete homomorphism f ϕ ∗ : L...

admitting a total lattice homomorphism to {⊥,⊤} must be Boolean. A standard workaround is to study maximal partial homomorphisms q with a filtering property:...

defines an injective homomorphism of normed algebras from C {\displaystyle \mathbb {C} } into the quaternions. Under this homomorphism, q is the image of...

with the multiplication), and is therefore a field homomorphism. The existence of this homomorphism makes fields in characteristic p quite different from...

\ast \colon Q\times Q\to Q} , called its multiplication, satisfying a distributive property such that x ∗ ( ⋁ i ∈ I y i ) = ⋁ i ∈ I ( x ∗ y i ) {\displaystyle...