Diego Vaggione

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We study direct product representations of algebras in varieties. We collect several conditions expressing that these representations are definable in a first-orderlogic sense, among them the concept of Definable Factor Congruences (DFC). The main results are that DFC is a Mal’cev property and that it is equivalent to all other conditions formulated; in(More)
Let A be an algebra. We use Con(A) to denote the congruence lattice of A. We say that θ, δ ∈ Con(A) permute if θ∨δ = {(x, y) ∈ A: there is z ∈ A such that (x, z) ∈ θ and (z, y) ∈ δ}. The algebra A is congruence permutable (permutable for short) if every pair of congruences in Con(A) permutes. By a system on A we understand a 2n-tuple (θ1, . . . , θn;x1, . .(More)
We study the following problem: Determine which almost structurally complete quasivarieties are structurally complete. We propose a general solution to this problem and then a solution in the semisimple case. As a consequence, we obtain a characterization of structurally complete discriminator varieties. An interesting corollary in logic follows: Let L be a(More)
The notion of central idempotent elements in a ring can be easily generalized to the setting of any variety with the property that proper subalgebras are always nontrivial. We will prove that if such a variety is also congruence modular, then it has factorable congruences, i.e., it has the FraserHorn property. (This property is well known to have major(More)