Geodesic
Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts
Bulletin of the Section of Logic, Tome 45 (2016) no. 3-4.

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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.
Keywords: universal algebra, algebraic lattice, congruence lattice, atomic lattice, modular lattice, uniform lattice, subdirect product, star-product, decomposition of algebra 
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     author = {Staruch, Bogdan and Staruch, Bo\.zena},
     title = {Decomposition of {Congruence} {Modular} {Algebras} into {Atomic,} {Atomless} {Locally} {Uniform} and {Anti-Uniform} {Parts}},
     journal = {Bulletin of the Section of Logic},
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Staruch, Bogdan; Staruch, Bożena. Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts. Bulletin of the Section of Logic, Tome 45 (2016) no. 3-4. http://geodesic.mathdoc.fr/item/BSL_2016_45_3-4_a1/