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Monotone-Cevian and finitely separable lattices
Miroslav Ploscica, Friedrich Wehrung
A distributive lattice with zero is completely normal if its prime ideals form a root system under set inclusion.Every such lattice admits a binary operation (x,y) \mapsto x-y sati…
A solution to the MV-spectrum Problem in size aleph one
Miroslav Ploscica, Friedrich Wehrung
Denote by Id the lattice of all principal -ideals of an Abelian -group . Our main result is the following. Theorem. For every countable Abelian -group $G…
Spectral subspaces of spectra of Abelian lattice-ordered groups in size aleph one
Miroslav Ploscica, Friedrich Wehrung
It is well known that the lattice Idc G of all principal {\ell}-ideals of any Abelian {\ell}-group G is a completely normal distributive 0-lattice, and that not every completely no…
Congruence pairs of principal MS-algebras and perfect extensions
Abd El-Mohsen Badawy, Miroslav Haviar, Miroslav Ploščica
The notion of a congruence pair for principal MS-algebras, simpler than the one given by Beazer for -algebras \cite{6}, is introduced. It is proved that the congruences of the…
Perfect extensions of de Morgan algebras
Miroslav Haviar, Miroslav Ploščica
An algebra is called a perfect extension of its subalgebra if every congruence of has a unique extension to . This terminology was us…