Irredundant Decomposition of Algebras into One-Dimensional Factors
MetadataShow full item record
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 subdirect product. We obtain the star-decomposition of algebras into one-dimensional factors, which generalizes the known decomposition theorems e.g. for Abelian groups, linear spaces, Boolean algebras.
Showing items related by title, author, creator and subject.
Bartoszewicz, Artur; Filipczak, Małgorzata; Prus-Wiśniowski, Franciszek (Wydawnictwo Uniwersytetu Łódzkiego, 2013)
Voutsadakis, George (Wydawnictwo Uniwersytetu Łódzkiego, 2015)Wójcicki introduced in the late 1970s the concept of a referential semantics for propositional logics. Referential semantics incorporate features of the Kripke possible world semantics for modal logics into the realm of ...
Dzik, Wojciech; Wróbel, Beniamin (Wydawnictwo Uniwersytetu Łódzkiego, 2015)Unifiability of terms (and formulas) and structural completeness in the variety of relation algebras RA and in the products of modal logic S5 is investigated. Nonunifiable terms (formulas) which are satisfiable in varieties ...