Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts

Bogdan Staruch; Bożena Staruch

doi:10.18778/0138-0680.45.3.4.05

Authors

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

DOI:

https://doi.org/10.18778/0138-0680.45.3.4.05

Keywords:

universal algebra, algebraic lattice, congruence lattice, atomic lattice, modular lattice, uniform lattice, subdirect product, star-product, decomposition of algebra

Abstract

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 consider four properties of lattices: atomic, atomless, locally uniform and anti-uniform. In effect, we describe a star-decomposition of a given algebra with modular congruence lattice into two or three parts associated to these properties.

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