Algebra and Logic Seminar - 5/11/2014

Wednesday, 5 November 2014, 3:15 p.m.

Lecturer: Prof. Thomas Scott Blyth (University of St. Andrews)

Title: "On ideals and congruences of distributive demi-p-algebras"

Local: Room 1.13, Edifício VII
Faculdade de Ciências e Tecnologia, Quinta da Torre, Caparica

Abstract: We identify the $\star$-ideals of a distributive demi-pseudocomplemented algebra $L$ as the kernels of the boolean congruences on $L$, and show that they form a complete Heyting algebra which is isomorphic to the interval $[G; \iota]$ of the congruence lattice of $L$ where $G$ is the Glivenko congruence. We also show that the notions of maximal $\star$-ideal, prime $\star$-ideal, and falsity ideal coincide.