Geodesic
Irredundant Decomposition of Algebras into One-Dimensional Factors
Bulletin of the Section of Logic, Tome 45 (2016) no. 3-4 Cet article a éte moissonné depuis la source Library of Science

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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.
Keywords: universal algebra, algebraic lattice, congruence lattice, uniform lattice, dimension of algebra, one-dimensional algebra, subdirect product, star-product, decomposition of algebra 
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     author = {Staruch, Bogdan},
     title = {Irredundant {Decomposition} of {Algebras} into {One-Dimensional} {Factors}},
     journal = {Bulletin of the Section of Logic},
     year = {2016},
     volume = {45},
     number = {3-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2016_45_3-4_a3/}
}
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Staruch, Bogdan. Irredundant Decomposition of Algebras into One-Dimensional Factors. Bulletin of the Section of Logic, Tome 45 (2016) no. 3-4. http://geodesic.mathdoc.fr/item/BSL_2016_45_3-4_a3/