Partial groupoid

In abstract algebra, a partial groupoid (also called halfgroupoid, pargoid, or partial magma) is a set endowed with a partial binary operation.[1][2]

A partial groupoid is a partial algebra.

Partial semigroup

A partial groupoid is called a partial semigroup if the following associative law holds:[3]

Let such that and , then

  1. if and only if
  2. and if (and, because of 1., also ).

References

  1. Evseev, A. E. (1988). "A survey of partial groupoids". In Ben Silver (ed.). Nineteen Papers on Algebraic Semigroups. American Mathematical Soc. ISBN 0-8218-3115-1.
  2. Folkert Müller-Hoissen; Jean Marcel Pallo; Jim Stasheff, eds. (2012). Associahedra, Tamari Lattices and Related Structures: Tamari Memorial Festschrift. Springer Science & Business Media. pp. 11 and 82. ISBN 978-3-0348-0405-9.
  3. Shelp, R. H. (1972). "A Partial Semigroup Approach to Partially Ordered Sets". Proc. London Math. Soc. (1972) s3-24 (1). London Mathematical Soc. pp. 46–58.

Further reading

  • E.S. Ljapin; A.E. Evseev (1997). The Theory of Partial Algebraic Operations. Springer Netherlands. ISBN 978-0-7923-4609-8.


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