dc.creator | Galatos, Nikolaos | |
dc.date.accessioned | 2020-08-22T00:17:04Z | |
dc.date.available | 2004-04-14 | |
dc.date.issued | 2003-04-14 | |
dc.identifier.uri | https://etd.library.vanderbilt.edu/etd-03312003-141423 | |
dc.identifier.uri | http://hdl.handle.net/1803/11794 | |
dc.description.abstract | A residuated lattice is an algebraic structure that has a lattice and a monoid reduct, such that multiplication is residuated with respect to the order. Residuated lattices generalize many well
studied algebras including lattice-ordered groups, Brouwerian algebras and generalized MV-algebras.
Moreover, they are connected to sub-structural logic, since they constitute algebraic semantics
for the unbounded full Lambek calculus.
Residuated lattices form a variety. We investigate the lattice of its subvarieties and concentrate
on a number of interesting subvarieties. In particular, we construct a continuum of
atomic varieties and prove that the join of two finitely based commutative residuated-lattice
varieties is also finitely based. Moreover, we study the varieties of cancellative and
of distributive residuated lattices and present a duality theory for the bounded members of the latter.
Finally, we generalize standard MV-algebras and describe a representation theorem and
a categorical equivalence about them.
As a corollary we obtain the decidablility of their equational theory. | |
dc.format.mimetype | application/pdf | |
dc.subject | variety | |
dc.subject | distributive | |
dc.subject | residuated lattices | |
dc.subject | cancellative | |
dc.subject | MV-algebras | |
dc.subject | subvariety lattice | |
dc.title | Varieties of residuated lattices | |
dc.type | dissertation | |
dc.contributor.committeeMember | Ralph McKenzie | |
dc.contributor.committeeMember | Steven Tschantz | |
dc.contributor.committeeMember | Jonathan Farley | |
dc.contributor.committeeMember | Alan Peters | |
dc.type.material | text | |
thesis.degree.name | PHD | |
thesis.degree.level | dissertation | |
thesis.degree.discipline | Mathematics | |
thesis.degree.grantor | Vanderbilt University | |
local.embargo.terms | 2004-04-14 | |
local.embargo.lift | 2004-04-14 | |
dc.contributor.committeeChair | Constantine Tsinakis | |