What is the name for f(ab)=f(b)f(a)?

  • Context: Graduate 
  • Thread starter Thread starter mnb96
  • Start date Start date
Click For Summary
SUMMARY

The concept where f(ab) = f(b)f(a) is known as an anti-homomorphism. This term is used in the context of group theory, particularly when discussing element inversion, as exemplified by the equation (ab)^{-1} = b^{-1}a^{-1}. An anti-homomorphism is a structure-preserving mapping that reverses the order of multiplication. This discussion clarifies the terminology and provides a specific example relevant to group theory.

PREREQUISITES
  • Understanding of group theory concepts
  • Familiarity with morphisms and their properties
  • Knowledge of element inversion in algebraic structures
  • Basic comprehension of mathematical notation and terminology
NEXT STEPS
  • Research the properties of anti-homomorphisms in algebra
  • Explore examples of anti-homomorphisms in various algebraic structures
  • Study the implications of anti-homomorphisms in group theory
  • Learn about related concepts such as isomorphisms and endomorphisms
USEFUL FOR

Mathematicians, students of abstract algebra, and anyone studying group theory or related algebraic structures will benefit from this discussion.

mnb96
Messages
711
Reaction score
5
Hi,
a morphism f is a structure preserving mapping, and under a morphism the following holds: f(ab) = f(a)f(b)

what is the name for a similar concept but where instead we have:
f(ab) = f(b)f(a)

This happens for example for the element inversion in a group: [tex](ab)^{-1}=b^{-1}a^{-1}[/tex].
I found it somewhere, some time ago, but I cannot find it anymore. I thought it was something like antimorphism, but I would not bet a cent on it.
 
Physics news on Phys.org
ok...I found it: it was anti-homomorphism
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 13 ·
Replies
13
Views
3K
  • · Replies 0 ·
Replies
0
Views
1K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 26 ·
Replies
26
Views
2K
Replies
2
Views
2K