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Two Infinite Sequences of Pre-Maximal Extensions of the Relevant Logic E
(Wydawnictwo Uniwersytetu Łódzkiego, 2019)
The only maximal extension of the logic of relevant entailment E is the classical logic CL. A logic L ⊆ [E,CL] called pre-maximal if and only if L is a coatom in the interval [E,CL]. We present two denumerable infinite ...
Irredundant Decomposition of Algebras into One-Dimensional Factors
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)
We introduce a notion of dimension of an algebraic lattice and, treating such a lattice as the congruence lattice of an algebra, we introduce the dimension of an algebra, too. We define a star-product as a special kind of ...
Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts
(Wydawnictwo Uniwersytetu Łódzkiego, 2016)
We describe here a special subdirect decomposition of algebras with modular congruence lattice. Such a decomposition (called a star-decomposition) is based on the properties of the congruence lattices of algebras. We ...
On the Category of EQ-algebras
(Wydawnictwo Uniwersytetu Łódzkiego, 2021-01-20)
In this paper, we studied the category of EQ-algebras and showed that it is complete, but it is not cocomplete, in general. We proved that multiplicatively relative EQ-algebras have coequlizers and we calculated coproduct ...