anti-isomorphism
Let and be rings and be a function such that for all .
If is a homomorphism of the additive groups of and , then is called an anti-homomorphsim.
If is a bijection and anti-homomorphism, then is called an anti-isomorphism.
If is an anti-homomorphism and then is called an anti-endomorphism.
If is an anti-isomorphism and then is called an anti-automorphism.
As an example, when , the mapping that sends a matrix to its transpose (or to its conjugate transpose if the matrix is complex) is an anti-isomorphism of .
and are anti-isomorphic if there is an anti-isomorphism .
All of the things defined in this entry are also defined for groups.
Title | anti-isomorphism |
---|---|
Canonical name | Antiisomorphism |
Date of creation | 2013-03-22 16:01:08 |
Last modified on | 2013-03-22 16:01:08 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 15 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 13B10 |
Classification | msc 16B99 |
Defines | anti-endomorphism |
Defines | anti-homomorphism |
Defines | anti-isomorphic |
Defines | anti-automorphism |