A354496 Number of left-sided quantales on n elements, up to isomorphism. Also number of right-sided quantales on n elements, up to isomorphism.

1, 2, 9, 60, 497, 4968, 58507, 807338, 13341730

Offset: 1

Author

Arman Shamsgovara, Aug 03 2022

Keywords

• nonn
• more

Comments

For definition of quantale see A354493.

A quantale is left-sided if every element x satisfies T * x <= x, and right-sided if every element x satisfies x * T <= x. Here T denotes the top element of the underlying lattice.

Transposition of the semigroup table yields a bijection between left-sided and right-sided quantales, so this sequence counts either type.

References

• P. Eklund, J. G. García, U. Höhle, and J. Kortelainen, (2018). Semigroups in complete lattices. In Developments in Mathematics (Vol. 54). Springer Cham.
• K. I. Rosenthal, Quantales and their applications. Longman Scientific and Technical, 1990.
• Arman Shamsgovara, A catalogue of every quantale of order up to 9 (abstract), LINZ2022, 39th Linz Seminar on Fuzzy Set Theory, Linz, Austria.

Crossrefs

Cf. A354493.