Partial algebra explained

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]

Further reading

• Book: Peter Burmeister. A Model Theoretic Oriented Approach to Partial Algebras. 2002. 1986. 10.1.1.92.6134.
• Book: Horst Reichel. Structural induction on partial algebras. 1984. Akademie-Verlag.
• Book: Horst Reichel. Initial computability, algebraic specifications, and partial algebras. 1987. Clarendon Press. 978-0-19-853806-6.

Notes and References

1. Book: Ivo G. Rosenberg . Gert Sabidussi. Algebras and Orders. 1993. Springer Science & Business Media. 978-0-7923-2143-9. Peter Burmeister. Partial algebras—an introductory survey . 1–70.
2. Book: George A. Grätzer. Universal Algebra. registration. 2008. Springer Science & Business Media. 978-0-387-77487-9. Chapter 2. Partial algebras. 2nd.
3. 10.1007/BF02283036. Effect algebras and unsharp quantum logics. Foundations of Physics. 24. 10. 1331. 1994. Foulis . D. J.. Bennett . M. K.. 10338.dmlcz/142815. 123349992. free.