scholarly journals Congruence permutability is prime

2021 ◽  
Author(s):  
Gergő Gyenizse ◽  
Miklós Maróti ◽  
Lászlo Zádori
Keyword(s):  
Congruence Permutability

Quasivarieties and Congruence Permutability of Łukasiewicz Implication Algebras

Studia Logica ◽  
2011 ◽  
Vol 98 (1-2) ◽  
pp. 267-283 ◽  
Author(s):  
M. Campercholi ◽  
D. Castaño ◽  
J. P. Díaz Varela
Keyword(s):  
Congruence Permutability ◽  
Implication Algebras ◽  
Łukasiewicz Implication Algebras

scholarly journals Congruence permutability for algebras with pseudocomplementation

1981 ◽  
Vol 24 (1) ◽  
pp. 55-58 ◽  
Author(s):  
R. Beazer
Keyword(s):  
Distributive Lattice ◽  
Congruence Lattice ◽  
Short Proof ◽  
Equational Class ◽  
Modular Lattices ◽  
Congruence Permutability ◽  
Congruence Relations ◽  
Necessary And Sufficient

In this note we are concerned with the permutability of congruence relations on semilattices and lattices with pseudocomplementation. There are some results in the literature along these lines. For example, in (8) H. P. Sankappanavar characterises those pseudocomplemented semilattices whose congruence lattice is modular and employs the result in conjunction with the well-known fact that algebras with permuting congruences are congruence-modular to characterise those pseudocomplemented semilattices with permuting congruences. Our first result is a direct, short proof of his result. In (2), J. Berman shows that for all congruences on a distributive lattice L with pseudocomplementation to permute it is necessary and sufficient that D(L), the dense filter of L, be relatively complemented. Our second result is a generalisation of that result to an important equational class of lattices with pseudocomplementation which properly contains the modular lattices with pseudocomplementation.

A note on congruence permutability and fuzzy logic

2005 ◽  
Vol 10 (3) ◽  
pp. 279-284 ◽  
Author(s):  
Vilém Vychodil
Keyword(s):  
Fuzzy Logic ◽  
Congruence Permutability
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