Irredundant Decomposition of Algebras into One-Dimensional Factors

Bogdan Staruch

Bulletin of the Section of Logic (2016)

  • Volume: 45, Issue: 3/4
  • ISSN: 0138-0680

Abstract

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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.

How to cite

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Bogdan Staruch. "Irredundant Decomposition of Algebras into One-Dimensional Factors." Bulletin of the Section of Logic 45.3/4 (2016): null. <http://eudml.org/doc/295509>.

@article{BogdanStaruch2016,
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.},
author = {Bogdan Staruch},
journal = {Bulletin of the Section of Logic},
keywords = {universal algebra; algebraic lattice; congruence lattice; uniform lattice; dimension of algebra; one-dimensional algebra; subdirect product; star-product; decomposition of algebra},
language = {eng},
number = {3/4},
pages = {null},
title = {Irredundant Decomposition of Algebras into One-Dimensional Factors},
url = {http://eudml.org/doc/295509},
volume = {45},
year = {2016},
}

TY - JOUR
AU - Bogdan Staruch
TI - Irredundant Decomposition of Algebras into One-Dimensional Factors
JO - Bulletin of the Section of Logic
PY - 2016
VL - 45
IS - 3/4
SP - null
AB - 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.
LA - eng
KW - universal algebra; algebraic lattice; congruence lattice; uniform lattice; dimension of algebra; one-dimensional algebra; subdirect product; star-product; decomposition of algebra
UR - http://eudml.org/doc/295509
ER -

References

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  19. [19] A. P. Zolotarev, Direct decompositions of elements, and Goldie numbers in balanced lattices, Russian Math. (Iz. VUZ), 36:10 (1992), pp. 19-27. 

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