Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts
Bogdan Staruch; Bożena Staruch
Bulletin of the Section of Logic (2016)
- Volume: 45, Issue: 3/4
- ISSN: 0138-0680
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topBogdan Staruch, and Bożena Staruch. "Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts." Bulletin of the Section of Logic 45.3/4 (2016): null. <http://eudml.org/doc/295564>.
@article{BogdanStaruch2016,
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.},
author = {Bogdan Staruch, Bożena Staruch},
journal = {Bulletin of the Section of Logic},
keywords = {universal algebra; algebraic lattice; congruence lattice; atomic lattice; modular lattice; uniform lattice; subdirect product; star-product; decomposition of algebra},
language = {eng},
number = {3/4},
pages = {null},
title = {Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts},
url = {http://eudml.org/doc/295564},
volume = {45},
year = {2016},
}
TY - JOUR
AU - Bogdan Staruch
AU - Bożena Staruch
TI - Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts
JO - Bulletin of the Section of Logic
PY - 2016
VL - 45
IS - 3/4
SP - null
AB - 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.
LA - eng
KW - universal algebra; algebraic lattice; congruence lattice; atomic lattice; modular lattice; uniform lattice; subdirect product; star-product; decomposition of algebra
UR - http://eudml.org/doc/295564
ER -
References
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- [3] G. Grätzer, General Lattice Theory. Second edition. Birkhauser Verlag, Basel (1998).
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- [6] J. Krempa, On lattices, modules and groups with many uniform elements, Algebra Discrete Math., 1 (2004), pp. 75–86.
- [7] E. R. Puczyłowski, A linear property of Goldie dimension of modules and modular lattices, J. Pure Appl. Algebra 215 (2011), pp. 1596–1605.
- [8] B. Staruch, Irredundant decomposition of algebras into one-dimensional factors, submitted to Bulletin of the Section of Logic (2016).
- [9] A. P. Zolotarev, On balanced lattices and Goldie dimension of balanced lattices, Siberian Math. J., 35:3 (1994), pp. 539–546.
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