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

1,2

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.

Links

Table of n, a(n) for n=1..9.

Crossrefs

Cf. A354493.

Sequence in context: A205570 A116364 A354314 * A357683 A120970 A339360

Adjacent sequences: A354493 A354494 A354495 * A354497 A354498 A354499

Keyword

nonn,more

Author

Arman Shamsgovara, Aug 03 2022

Status

approved