Irredundant Decomposition of Algebras into One-Dimensional Factors

Bogdan Staruch

doi:10.18778/0138-0680.45.3.4.06

Authors

Bogdan Staruch University of Warmia and Mazury, Olsztyn, Department of Mathematics and Computer Science Author

DOI:

https://doi.org/10.18778/0138-0680.45.3.4.06

Keywords:

universal algebra, algebraic lattice, congruence lattice, uniform lattice, dimension of algebra, one-dimensional algebra, subdirect product, star-product, decomposition of algebra

Abstract

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.

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