Definitions For Automorphism

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

Derived terms

automorphism group

Translations

Catalan: automorfisme, m Danish: automorfi, c Finnish: automorfismi German: Automorphismus, m Icelandic: sjálfmótun, f Irish: uathmhorfacht, f Italian: automorfismo, m Portuguese: automorfismo, m Russian: автоморфи́зм, m Serbo-Croatian: automorfizam, m Spanish: automorfismo, m Swedish: automorfi, automorfism