Automorphism
Definition
An isomorphism defined from a mathematical object (group, ring, vector space, graph) or algebraic structure onto itself, establishing a structural bijection that preserves all characteristic internal operations and relations. In modern geometry and algebra, an automorphism represents an absolute internal symmetry of the structure, mapping system elements in a reflexive way that leaves its fundamental laws of composition unchanged.
Bilingual Equivalents
- Automorphism
- Self-isomorphism
Grammatical & Source Details
| Inflection Type | Neuter noun, taking regular plural structural forms ending in '-isme'. |
| Formation | Compound structure built from the prefixoid 'auto-' and the noun 'morfism' (morphism). |
| Spelling / Pronunciation | [a.u.to.mor.ˈfism] |
| Source | Lexicon of Advanced Mathematics, Topology, and Algebraic Structure Theories |
Contextual Usage Examples
RO: Profesorul a demonstrat că mulțimea tuturor automorfismelor unui grup formează un grup sub operația de compunere.
EN: The professor demonstrated that the set of all automorphisms of a group forms a group under the composition operation.
RO: În geometria diferențială, un automorfism liniar conservă distanțele și unghiurile din spațiul vectorial.
EN: In differential geometry, a linear automorphism preserves distances and angles within the vector space.
RO: Fiecare automorfism aplicat acestui graf lasă neschimbată matricea de adiacență a nodurilor.
EN: Every automorphism applied to this graph leaves the adjacency matrix of the nodes unchanged.
Idioms & Phrases
Grup de automorfisme / Automorphism group
RO: Structură algebrică constituită din totalitatea transformărilor bijective autoreferențiale ale unui obiect matematic.
EN: An algebraic structure consisting of the totality of self-referential bijective transformations of a mathematical object.
Automorfism interior / Inner automorphism
RO: Automorfism special al unui grup realizat prin conjugarea elementelor sale cu un element fix din același grup.
EN: A special automorphism of a group achieved by conjugating its elements with a fixed element from the same group.
Automorfism analitic / Analytic automorphism
RO: Funcție bijectivă și olomorfă definită de la un spațiu complex pe el însuși, utilizată în teoria funcțiilor complexe.
EN: A bijective and holomorphic function defined from a complex space onto itself, used in complex function theory.
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