9 papers
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…
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…
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…
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…