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by Ciro Santilli (@cirosantilli, 37)

Isomorphism

 Home Mathematics Area of mathematics Algebra Group Group isomorphism
 1 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my version
Something analogous to a group isomorphism, but that preserves whatever properties the given algebraic object has. E.g. for a field, we also have to preserve multiplication in addition to addition.
Other common examples include isomorphisms of vector spaces and field. But since both of those two are much simpler than groups in classification, as they are both determined by number of elements/dimension alone, see:
  • classification of finite fields
  • all vector spaces of the same dimension on a given field are isomorphic
we tend to not talk about isomorphisms so much in those contexts.

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  • All indefinite orthogonal groups of matrices of equal metric signature are isomorphic

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Isomorphism by Wikipedia Bot 0  1970-01-01
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