Nagata products of bimodules over residuated lattices

Adam Přenosil; Constantine Tsinakis

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arXiv · 2505.11479

Nagata products of bimodules over residuated lattices

Adam Přenosil·Constantine Tsinakis

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Abstract

We study the (restricted) Nagata product construction, which produces a partially ordered semigroup from a bimodule consisting of a partially ordered semigroup acting on a (pointed) join semilattice. A canonical example of such a bimodule is given by a residuated lattice acting on itself by division, in which case the Nagata product coincides with the so-called twist product of the residuated lattice. We show that, given some further structure, a pointed bimodule can be reconstructed from its restricted Nagata product. This yields an adjunction between the category of cyclic pointed residuated bimodules and a certain category of posemigroups with additional structure, which subsumes various known adjunctions involving the twist product construction.

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BibTeX RIS

Adam Přenosil, Constantine Tsinakis. 2025-05-16. Nagata products of bimodules over residuated lattices. https://arxiv.org/abs/2505.11479

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