Projectivity in (bounded) integral residuated lattices [article]

Paolo Aglianò, Sara Ugolini
2022 arXiv   pre-print
In this paper we study projective algebras in varieties of (bounded) commutative integral residuated lattices from an algebraic (as opposed to categorical) point of view. In particular we use a well-established construction in residuated lattices: the ordinal sum. Its interaction with divisibility makes our results have a better scope in varieties of divisibile commutative integral residuated lattices, and it allows us to show that many such varieties have the property that every finitely
more » ... ted algebra is projective. In particular, we obtain results on (Stonean) Heyting algebras, certain varieties of hoops, and product algebras. Moreover, we study varieties with a Boolean retraction term, showing for instance that in a variety with a Boolean retraction term all finite Boolean algebras are projective. Finally, we connect our results with the theory of Unification.
arXiv:2008.13181v4 fatcat:6z763xftljhsbnhbplmhwuesru