A note on congruence systems of MS-algebras. (English) Zbl 1174.06312

Campercholi, M.; Vaggione, D.

Math. Bohem. 132, No. 4, 337-343 (2007).

Summary: Let \(L\) be an MS-algebra with congruence permutable skeleton. We prove that solving a system of congruences \((\theta _{1},\dots ,\theta _{n};x_{1} ,\dots ,x_{n})\) in \(L\) can be reduced to solving the restriction of the system to the skeleton of \(L\), plus solving the restrictions of the system to the intervals \([x_{1},\bar {\bar x}_{1}],\dots ,[x_{n},\bar { \bar x}_{n}].\)

MSC:

06D30

De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)

Keywords:

MS-algebra; permutable congruence; congruence system