## Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts

dc.contributor.author | Staruch, Bogdan | |

dc.contributor.author | Staruch, Bożena | |

dc.date.accessioned | 2017-07-10T12:08:38Z | |

dc.date.available | 2017-07-10T12:08:38Z | |

dc.date.issued | 2016 | |

dc.identifier.issn | 0138-0680 | |

dc.identifier.uri | http://hdl.handle.net/11089/22186 | |

dc.description.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. | en_GB |

dc.language.iso | en | en_GB |

dc.publisher | Wydawnictwo Uniwersytetu Łódzkiego | en_GB |

dc.relation.ispartofseries | Bulletin of the Section of Logic;3/4 | |

dc.subject | universal algebra | en_GB |

dc.subject | algebraic lattice | en_GB |

dc.subject | congruence lattice | en_GB |

dc.subject | atomic lattice | en_GB |

dc.subject | modular lattice | en_GB |

dc.subject | uniform lattice | en_GB |

dc.subject | subdirect product | en_GB |

dc.subject | star-product | en_GB |

dc.subject | decomposition of algebra | en_GB |

dc.title | Decomposition of Congruence Modular Algebras into Atomic, Atomless Locally Uniform and Anti-Uniform Parts | en_GB |

dc.type | Article | en_GB |

dc.rights.holder | © Copyright by Authors, Łódź 2016; © Copyright for this edition by Uniwersytet Łódzki, Łódź 2016 | en_GB |

dc.page.number | [199]-211 | |

dc.contributor.authorAffiliation | University of Warmia and Mazury, Olsztyn, Department of Mathematics and Computer Science | |

dc.identifier.eissn | 2449-836X | |

dc.references | S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, (1981). | en_GB |

dc.references | A.W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3), 8 (1958), pp. 589–608. | en_GB |

dc.references | G. Grätzer, General Lattice Theory. Second edition. Birkhauser Verlag, Basel (1998). | en_GB |

dc.references | P. Grzeszczuk, E. R. Puczyłowski, On Goldie and dual Goldie dimensions, J. Pure Appl. Algebra 31 (1984), pp. 47–54. | en_GB |

dc.references | P. Grzeszczuk, E. R. Puczyłowski, On infinite Goldie dimension of modular lattices and modules, J. Pure Appl. Algebra 35 (1985), pp. 151–155. | en_GB |

dc.references | J. Krempa, On lattices, modules and groups with many uniform elements, Algebra Discrete Math., 1 (2004), pp. 75–86. | en_GB |

dc.references | E. R. Puczyłowski, A linear property of Goldie dimension of modules and modular lattices, J. Pure Appl. Algebra 215 (2011), pp. 1596–1605. | en_GB |

dc.references | B. Staruch, Irredundant decomposition of algebras into one-dimensional factors, submitted to Bulletin of the Section of Logic (2016). | en_GB |

dc.references | A. P. Zolotarev, On balanced lattices and Goldie dimension of balanced lattices, Siberian Math. J., 35:3 (1994), pp. 539–546. | en_GB |

dc.contributor.authorEmail | bstar@uwm.edu.pl | |

dc.contributor.authorEmail | bostar@matman.uwm.edu.pl | |

dc.identifier.doi | 10.18778/0138-0680.45.3.4.05 | |

dc.relation.volume | 45 | en_GB |