Geodesic
Irredundant Decomposition of Algebras into One-Dimensional Factors
Bulletin of the Section of Logic, Tome 45 (2016) no. 3-4.

Voir la notice de l'article provenant de la source Library of Science

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 
@article{BSL_2016_45_3-4_a3,
     author = {Staruch, Bogdan},
     title = {Irredundant {Decomposition} of {Algebras} into {One-Dimensional} {Factors}},
     journal = {Bulletin of the Section of Logic},
     publisher = {mathdoc},
     volume = {45},
     number = {3-4},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BSL_2016_45_3-4_a3/}
}
TY  - JOUR
AU  - Staruch, Bogdan
TI  - Irredundant Decomposition of Algebras into One-Dimensional Factors
JO  - Bulletin of the Section of Logic
PY  - 2016
VL  - 45
IS  - 3-4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BSL_2016_45_3-4_a3/
LA  - en
ID  - BSL_2016_45_3-4_a3
ER  - 
%0 Journal Article
%A Staruch, Bogdan
%T Irredundant Decomposition of Algebras into One-Dimensional Factors
%J Bulletin of the Section of Logic
%D 2016
%V 45
%N 3-4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BSL_2016_45_3-4_a3/
%G en
%F BSL_2016_45_3-4_a3
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/