Automorphism

Quick meaning: Automorphism is a noun meaning (algebra) An isomorphism of a mathematical object or system of objects onto itself.

Meaning

(algebra) An isomorphism of a mathematical object or system of objects onto itself.

More Meanings

1. The ascription to others of one's own characteristics or of one's own perceived characteristics.

Example Sentences

A tame automorphism is a product of elementary automorphisms, and a non-tame automorphism is called wild. The “tame automorphism problem” asks whether any automorphism is tame.

In mathematics, automorphisms of algebraic structures play an important role. Automorphisms capture the symmetries inherent in the structures and many important results have been proved by analyzing the automorphism group of the structure.

Since every linear automorphism of V fixes 0 our interest in the transitivity properties of GL(V) is confined to its action on V* = V - {0}. GL(V) is transitive on V* since any two elements of V* may be chosen as the initial members of two ordered bases; it is not in general 2-transitive because there is no linear automorphism taking an independent pair to a dependent pair.

Word Forms

• automorphisms

Synonyms for automorphism

Depending on context, synonyms include projection, heautomorphism.

Related Words

Related dictionary entries include endomorphism, homomorphism, automorphy, antimorphism, isomorphism, antiautomorphism.

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