AUTOMORPHISM

Etymology

Noun

automorphism (plural automorphisms)

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

The ascription to others of one's own characteristics.

Usage notes

• (algebra)

An automorphism is characterised by the structure it preserves, which is usually specified as an object type. Thus one may speak of a group automorphism or ring automorphism.

The identity mapping is sometimes called the trivial automorphism; any other automorphism may then be called a nontrivial automorphism.

Synonyms

• (isomorphism of a mathematical object or system of objects onto itself): self-map

• (ascription to others of one's own characteristics): projection

Hypernyms

• (algebra): isomorphism, endomorphism

Hyponyms

• (algebra): inner automorphism, outer automorphism, Möbius transformation

Source: Wiktionary

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Au`to*mor"phism, n.

Definition: Automorphic characterization. H. Spenser.

Source: Webster’s Unabridged Dictionary 1913 Edition

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