Splittings in varieties of logic

We study splittings or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the non-splitting lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splitting algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double [Formula: see text]-algebras the only splitting algebras are the two-element and three-element chains.

MTL-algebras as rotations of basic hoops

In this paper, we use the generalize d rotation construction to lift results from the lattice of subvarieties of basic hoops to some parts of the lattice of subvarieties of monoidal t-norm based logic-algebras. In particular, we study splitting algebras for (the lattice of subvarieties of) varieties generated by generalized rotations of basic hoops and relevant subvarieties such as Wajsberg hoops, cancellative hoops and Gödel hoops. Finally, we show that the generalized rotation construction preserves the amalgamation property.

SPLITTING ALGEBRAS, SYMMETRIC FUNCTIONS AND GALOIS THEORY

We present a theory for splitting algebras of monic polynomials over rings, and apply the results to symmetric functions, and Galois theory.