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:
we tend to not talk about isomorphisms so much in those contexts.
Articles by others on the same topic
An isomorphism is a morphism that has a two-sided inverse. Two objects are isomorphic when an isomorphism exists between them.
Isomorphism is a concept that appears in various fields such as mathematics, computer science, and social science, and it generally refers to a kind of equivalence or similarity in structure between two entities. Here are a few specific contexts in which the term is often used: 1. **Mathematics**: In mathematics, particularly in algebra and topology, an isomorphism is a mapping between two structures that preserves the operations and relations of the structures.