Definitions

1. noun

A bijective homomorphism from a mathematical object to itself.

“The group’s automorphism was crucial in solving the complex algebraic equation.”

2. noun

A type of isomorphism that is also an automorphism of the underlying algebra.

“The abstract algebraist studied the automorphism of the group ring.”

3. noun

A mapping from a mathematical object to itself that preserves the structure or operations of the object.

“The researcher found an automorphism of the graph that preserved its symmetries.”

4. noun

A type of symmetry that preserves the structure of an object or a mathematical concept.

“The physicist discovered an automorphism of the crystal lattice that explained its unique properties.”

5. noun

A mathematical concept used to describe a type of symmetry in algebraic structures such as groups and rings.

“The mathematician used automorphisms to classify the symmetry of the algebraic structures.”