Varieties of BL-Algebras III: Splitting Algebras

Studia Logica ◽  
2018 ◽  
Vol 107 (6) ◽  
pp. 1235-1259 ◽  
Author(s):  
Paolo Aglianó
Keyword(s):  
Splitting Algebras

Splittings in varieties of logic

2021 ◽  
pp. 1-48
Author(s):  
Brian A. Davey ◽  
Tomasz Kowalski ◽  
Christopher J. Taylor
Keyword(s):  
Residuated Lattices ◽  
Heyting Algebras ◽  
General Lemma ◽  
Negative Results ◽  
Splitting Algebras

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.

Splitting algebras and Schubert calculus

2012 ◽  
Vol 61 (3) ◽  
pp. 1253-1312 ◽  
Author(s):  
Dan Laksov ◽  
Anders Thorup
Keyword(s):  
Schubert Calculus ◽  
Splitting Algebras

scholarly journals Splitting algebras: Koszul, Cohen–Macaulay and numerically Koszul

2015 ◽  
Vol 422 ◽  
pp. 660-682 ◽  
Author(s):  
Tyler Kloefkorn ◽  
Brad Shelton
Keyword(s):  
Splitting Algebras

MTL-algebras as rotations of basic hoops

2019 ◽  
Vol 29 (5) ◽  
pp. 763-784 ◽  
Author(s):  
Paolo Aglianò ◽  
Sara Ugolini
Keyword(s):  
Amalgamation Property ◽  
Lattice Of Subvarieties ◽  
Wajsberg Hoops ◽  
Splitting Algebras

Abstract 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.

scholarly journals SPLITTING ALGEBRAS, SYMMETRIC FUNCTIONS AND GALOIS THEORY

2005 ◽  
Vol 04 (01) ◽  
pp. 59-75 ◽  
Author(s):  
T. EKEDAHL ◽  
D. LAKSOV
Keyword(s):  
Symmetric Functions ◽  
Galois Theory ◽  
Splitting Algebras

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

scholarly journals Generic splitting algebras for Pic

1970 ◽  
Vol 35 (2) ◽  
pp. 369-380
Author(s):  
Gerald Garfinkel
Keyword(s):  
Splitting Algebras
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