A357294 - OEIS

%I #6 Nov 06 2022 12:27:43

%S 1,1,2,9,49,364,3335,37026,496241

%N Number of integral quantales on n elements, up to isomorphism.

%C For definition of quantale see A354493.

%C A quantale is integral if the top element in the underlying lattice is a unit element. Equivalently, it is both unital and balanced. Equivalently, it is both strictly left-sided and strictly right-sided.

%D P. Eklund, J. G. García, U. Höhle, and J. Kortelainen, (2018). Semigroups in complete lattices. In Developments in Mathematics (Vol. 54). Springer Cham.

%D K. I. Rosenthal, Quantales and their applications. Longman Scientific and Technical, 1990.

%D Arman Shamsgovara, A catalogue of every quantale of order up to 9 (abstract), LINZ2022, 39th Linz Seminar on Fuzzy Set Theory, Linz, Austria.

%D Arman Shamsgovara and P. Eklund, A Catalogue of Finite Quantales, GLIOC Notes, December 2019.

%Y Cf. A354493, A354495, A354497, A357295.

%K nonn,more

%O 1,3

%A _Arman Shamsgovara_, Sep 22 2022