Locally Integral Involutive PO-Semigroups

Authors

• José Gil-Férez, Chapman UniversityFollow
• Peter Jipsen, Chapman UniversityFollow
• Melissa Sugimoto, Chapman UniversityFollow

Document Type

Article

Publication Date

12-30-2025

Abstract

We show that every locally integral involutive partially ordered semigroup (ipo-semigroup) A=(A,≤,⋅,∼,−), and in particular every locally integral involutive semiring, decomposes in a unique way into a family {Ap:p∈A+} of integral ipo-monoids, which we call its integral components. In the semiring case, the integral components are unital semirings. Moreover, we show that there is a family of monoid homomorphisms Φ={φpq:Ap→Aq:p≤q}, indexed over the positive cone (A+,≤), so that the structure of A can be recovered as a glueing ∫ΦAp of its integral components along Φ. Reciprocally, we give necessary and sufficient conditions so that the Płonka sum of any family of integral ipo-monoids {Ap:p∈D}, indexed over a join-semilattice (D,∨) along a family of monoid homomorphisms Φ is an ipo-semigroup.

Comments

This article was originally published in Fundamenta Informaticae, volume 195, issue 1-4, in 2025. https://doi.org/10.46298/fi.12449

Recommended Citation

Gil-Férez J, Jipsen P, Sugimoto M. Locally integral involutive PO-semigroups. Fundamenta Informaticae 195: 1-29. URL doi.org/10.46298/fi.12449

Copyright

The authors