| |
|
Description: |
Profinite algebras have been extensively considered in the literature, particularly in the realms of groups and semigroups. They are the residually finite topological algebras over Stone spaces. In this talk, we consider classes of Stone topological algebras of a fixed signature that are closed under taking quotients that are again Stone spaces, closed subalgebras and finite direct products; we call such classes Stone pseudovarieties. This generalizes the usual notion of pseudovariety of finite algebras. We show how an arbitrary Stone topological algebra, both in its algebraic and topological structures, may be regarded as the dual of a Boolean algebra of subsets of a term algebra with a rather simple additional structure, providing an alternative approach to the duality theory of Gehrke. As an application, we generalize a result of Gehrke from the residually finite case to a general Stone pseudovariety: the class of all Stone topological algebras residually in a given Stone pseudovariety is again a Stone pseudovariety.
|
|
Date: |
|
| Start Time: |
16:00 |
|
Speaker: |
Jorge Almeida (CMUP, Univ. Porto)
|
|
Institution: |
University of Porto
|
|
Place: |
Sala 5.5
|
| Research Groups: |
-Algebra, Logic and Topology
|
|
See more:
|
<Main>
|
|
