10 papers
A completion of reduced commutative rings
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
A commutative ring is reduced when it can be embedded into a direct product of fields. While the category of reduced commutative rings plays a fundamental role in affine geometry,…
A categorical description of simple Beth companions
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
A pp expansion of a quasivariety is said to be simple when it is of the form . For instance, when has the amalgamatio…
Bounded depth in Hilbert algebras
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
Hilbert algebras are the implicative subreducts of Heyting algebras. It is shown that having depth at most n is an equational condition in Hilbert algebras. This generalizes an ana…
Ultracontact algebras and stack systems
Luca Carai, Ivo Düntsch, Rafał Gruszczyński +1
We study the class of structures that, in a way, generalize various approaches to the contact relation on Boolean algebras.
Implicit operations in varieties of commutative monoids
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
An implicit operation of a class of similar algebras is a collection of first order definable partial functions on the members of that is globally preserv…
An addendum to "The theory of implicit operations"
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
In this addendum to [4], we provide a pair of counterexamples relevant to the theory of implicit operations. More precisely, we exhibit a pp expansion of a variety that fails to be…
Congruence permutability in quasivarieties
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
It is shown that a natural notion of congruence permutability for quasivarieties already implies ``being a variety''. The result follows immediately from [3] and the sole aim of th…
The theory of implicit operations
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
A family of partial functions of a class of algebras is said to be an implicit operation of when it is defined by a first order formula and it is preserve…
On the universal theory of the free pseudocomplemented distributive lattice
Luca Carai, Tommaso Moraschini
It is shown that the universal theory of the free pseudocomplemented distributive lattice is decidable and a recursive axiomatization is presented. This contrasts with the case of…
Epimorphisms between finitely generated algebras
Luca Carai, Miriam Kurtzhals, Tommaso Moraschini
A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property…