# All idempotent hypersubstitutions of type (2,2)

@article{Cangpas2008AllIH,
title={All idempotent hypersubstitutions of type (2,2)},
author={Tawat Cangpas and Klaus Denecke},
journal={Semigroup Forum},
year={2008},
volume={76},
pages={525-539}
}
AbstractA hypersubstitution of type (2,2) is a map σ which takes the binary operation symbols f and g to binary terms σ(f) and σ(g). Any such σ can be inductively extended to a map $\hat{\sigma}$ on the set of all terms of type (2,2). By using this extension on the set Hyp(2,2) of all hypersubstitutions of type (2,2) a binary operation can be defined. Together with the identity hypersubstitution mapping f to f(x1,x2) and g to g(x1,x2) the set Hyp(2,2) forms a monoid. This monoid is isomorphic… CONTINUE READING

## The Order of Hypersubstitutions of Type (2, 1)

• Int. J. Math. Mathematical Sciences
• 2011