homomorphism's Usage Examples:

In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector.

In algebra, the kernel of a homomorphism (function that preserves the structure) is generally the inverse image of 0 (except for groups whose operation.

In mathematics, given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G.

the area of topology known as algebraic topology, an induced homomorphism is a homomorphism derived in a canonical way from another map.

In particular, a bounded-lattice homomorphism (usually called just "lattice homomorphism") f between two bounded lattices L and M should.

map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping V → W {\displaystyle.

from that of an injective homomorphism.

algebra, a ring homomorphism is a structure-preserving function between two rings.

More explicitly, if R and S are rings, then a ring homomorphism is a function.

Not every semigroup homomorphism between monoids is a monoid homomorphism, since it may not map the identity to the identity.

for any group homomorphism f : G → H {\displaystyle f:G\to H} .

Note that f op {\displaystyle f^{\text{op}}} is indeed a group homomorphism from G op {\displaystyle.

equivalence relation and the composition of loops, and we get a group homomorphism from π(X, x0) to π(Y, y0).

In mathematics, an algebra homomorphism is a homomorphism between two associative algebras.

groups, then a Lie group homomorphism f : G → H is a smooth group homomorphism.

In the case of complex Lie groups, such a homomorphism is required to be a.

However, a homomorphism between graphs is the same thing as a homomorphism between the two structures coding the graph.

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.

A *-homomorphism f : A → B is an algebra homomorphism that is compatible with the involutions of A and B.

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.

Though similar on objects, the terms entail different notions of homomorphism, as will be explained in the below section on morphisms.

In the mathematical field of graph theory, a graph homomorphism is a mapping between two graphs that respects their structure.

Synonyms:

homomorphy; similarity;

Antonyms:

similar; difference; dissimilarity;