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A354496
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Number of left-sided quantales on n elements, up to isomorphism. Also number of right-sided quantales on n elements, up to isomorphism.
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2
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OFFSET
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1,2
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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