Partial algebra

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

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. Peter Burmeister (1993). "Partial algebras—an introductory survey". In Ivo G. Rosenberg; Gert Sabidussi (eds.). 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.
3. Foulis, D. J.; Bennett, M. K. (1994). "Effect algebras and unsharp quantum logics". Foundations of Physics. 24 (10): 1331. Bibcode:1994FoPh...24.1331F. doi:10.1007/BF02283036. hdl:10338.dmlcz/142815. S2CID 123349992.

Further reading

• Peter Burmeister (2002) [1986]. A Model Theoretic Oriented Approach to Partial Algebras. CiteSeerX 10.1.1.92.6134.
• 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.