Partial algebra: Difference between revisions
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In [[abstract algebra]], a '''partial algebra''' is a generalization of [[universal algebra]] to [[partial function|partial]] [[Operation (mathematics)|operations]].<ref name="RosenbergSabidussi1993">{{cite book|editors=Ivo G. Rosenberg and Gert Sabidussi|title=Algebras and Orders|year=1993|publisher=Springer Science & Business Media|isbn=978-0-7923-2143-9|author=Peter Burmeister|chapter=Partial algebras - an introductory survey | pages= |
In [[abstract algebra]], a '''partial algebra''' is a generalization of [[universal algebra]] to [[partial function|partial]] [[Operation (mathematics)|operations]].<ref name="RosenbergSabidussi1993">{{cite book|editors=Ivo G. Rosenberg and Gert Sabidussi|title=Algebras and Orders|year=1993|publisher=Springer Science & Business Media|isbn=978-0-7923-2143-9|author=Peter Burmeister|chapter=Partial algebras - an introductory survey | pages=1–70}}</ref><ref name="Gratzer2008">{{cite book|author=George A. Grätzer|title=Universal Algebra|year=2008|publisher=Springer Science & Business Media|isbn=978-0-387-77487-9|at=Chapter 2. Partial algebras|edition=2nd}}</ref> |
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==Example(s)== |
==Example(s)== |
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Revision as of 20:04, 1 September 2014
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
- ^ a b c Peter Burmeister (1993). "Partial algebras - an introductory survey". Algebras and Orders. Springer Science & Business Media. pp. 1–70. ISBN 978-0-7923-2143-9.
{{cite book}}: Unknown parameter|editors=ignored (|editor=suggested) (help) - ^ George A. Grätzer (2008). Universal Algebra (2nd ed.). Springer Science & Business Media. Chapter 2. Partial algebras. ISBN 978-0-387-77487-9.
- ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1007/BF02283036, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with
|doi=10.1007/BF02283036instead.
Further reading
- Peter Burmeister (2002) [1986]. A Model Theoretic Oriented Approach to Partial Algebras (PDF).
- 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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