---
tag: N9M2N27END
kind: concept
name: Term operation
msc: [08A40]
sources:
  - url: https://en.wikipedia.org/wiki/Clone_(algebra)
---

## Summary

A term operation of an algebra is an operation on the algebra obtained by [[evaluating|DH30WTA26T]] a [[term|6D3WA7N2W4]] in it.
The term operations are exactly the operations that can be built from the basic operations and the projections by composition.
They form the clone of the algebra, and two algebras with the same term operations behave alike for most questions of universal algebra.

## Explanations

### L1 human

The basic operations of an algebra are the ones it comes with, such as $+$ and $\cdot$ in a ring.
Combining them gives new operations, such as $(x, y) \mapsto x \cdot x + y$, and these are the term operations.
In a group, $(x, y) \mapsto x y x^{-1}$ is a term operation, built from multiplication and inversion.
Fixed elements of the algebra may not be used as constants unless the signature names them.