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SUMMARY:Isis Gallardo (University of Denver)
DTSTART:20250313T180000Z
DTEND:20250313T190000Z
DTSTAMP:20260423T052759Z
UID:OLS/174
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OLS/174/">De
 cidability and generation of the variety of distributive $\\ell$-pregroups
 .</a>\nby Isis Gallardo (University of Denver) as part of Online logic sem
 inar\n\n\nAbstract\nLattice-ordered pregroups ($\\ell$-pregroups) represen
 t a natural generalization of lattice ordered groups ($\\ell$-groups). It 
 is well-established that every $\\ell$-group can be embedded into a symmet
 ric one\, as demonstrated by Cayley-Holland’s embedding theorem. Analogo
 usly\, a Cayley-Holland’s embedding theorem exists for distributive $\\e
 ll$-pregroups\, asserting that any distributive $\\ell$-pregroup can be em
 bedded into a functional one. In this work\, we enhance this result by est
 ablishing that any distributive $\\ell$-pregroup can be embedded into a fu
 nctional one over a chain that is locally isomorphic to $\\mathbb{Z}$. Uti
 lizing this\, we demonstrate that the variety of distributive $\\ell$-preg
 roups is generated by the (single) functional algebra over the integers. W
 e will later use this to prove the decidability of the variety.\n
LOCATION:https://researchseminars.org/talk/OLS/174/
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