Partial algebra

Short description: Algebraic structure

In abstract algebra, a partial algebra is a generalization of universal algebra to partial operations.[1][2]

## Contents

* 1 Example(s)
* 2 Structure
* 3 References
* 4 Further reading

## Example(s)

* partial groupoid
* field — the multiplicative inversion is the only proper partial operation[1]
* effect algebras[3]

## Structure

There is a "Meta Birkhoff Theorem" by Andreka, Nemeti and Sain (1982).[1]

## References

1. ↑ 1.0 1.1 1.2 Peter Burmeister (1993). "Partial algebras—an introductory survey". Algebras and Orders. Springer Science & Business Media. pp. 1–70. ISBN 978-0-7923-2143-9.
2. ↑ George A. Grätzer (2008). Universal Algebra (2nd ed.). Springer Science & Business Media. Chapter 2. Partial algebras. ISBN 978-0-387-77487-9. https://archive.org/details/isbn_9780387774862.
3. ↑ Foulis, D. J.; Bennett, M. K. (1994). "Effect algebras and unsharp quantum logics". Foundations of Physics 24 (10): 1331. doi:10.1007/BF02283036. Bibcode: 1994FoPh...24.1331F.

## Further reading

* Peter Burmeister (2002). A Model Theoretic Oriented Approach to Partial Algebras.
* Horst Reichel (1984). Structural induction on partial algebras. Akademie-Verlag.
* Horst Reichel (1987). Initial computability, algebraic specifications, and partial algebras. Clarendon Press. ISBN 978-0-19-853806-6.

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