Wednesday8Feb 2023

Schmid College Science Forum

The structure of locally integral involutive partially ordered monoids

Wednesday, February 8, 2023 12:00 p.m. - 1:00 p.m. PST
2023-02-08 12:00 2023-02-08 13:00 America/Los_Angeles Schmid College Science Forum Go to event listing for more details: https://events.chapman.edu/88498 AF 201 Argyros Forum 201 - Charles and Nora Hester Faculty Senate Boardroom

Free to attend

AF 201

Argyros Forum 201 - Charles and Nora Hester Faculty Senate Boardroom

Staff, Faculty, and Students

are invited to attend.

Join us for the Schmid College Science Forum Series featuring Dr. Jose Gil-Ferez.

Title: The structure of locally integral involutive partially ordered monoids

Abstract: In this lecture, we will introduce and study a certain type of mathematical structures called locally integral involutive partially ordered monoids (ipo-monoids, for short). Their relevance, among other things, resides in the fact that they constitute semantics for some nonclassical logics. We will demonstrate that every locally integral ipo-monoid A decomposes in a unique way into a family of integral ones, which we call its integral components. Moreover, we will associate to A a family of monoid homomorphisms (indexed on the order of the positive cone of A) so that the structure of A can be recovered as a glueing of its integral components along that family. Reciprocally, we will give necessary and sufficient conditions so that the Płonka sum of any family of integral ipo-monoids (indexed on a lower-bounded join-semilattice) along a family of monoid homomorphisms is an ipo-monoid.

 

 

 

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