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

• Autorzy: Bogdan Staruch , Bożena Staruch
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

universal algebra; algebraic lattice; congruence lattice; atomic lattice; modular lattice; uniform lattice; subdirect product; star-product; decomposition of algebra

• Wydawca: Wydawnictwo Uniwersytetu Łódzkiego
• Czasopismo: Bulletin of the Section of Logic
• Rocznik: 2016
• Tom: 45
• Numer: 3/4

Daty

wydano

2016-12-30

Twórcy

autor

Bogdan Staruch

• University of Warmia and Mazury, Olsztyn, Department of Mathematics and Computer Science

autor

Bożena Staruch

Bibliografia

• [1] S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer-Verlag, (1981).
• [2] A.W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3), 8 (1958), pp. 589–608.
• [3] G. Grätzer, General Lattice Theory. Second edition. Birkhauser Verlag, Basel (1998).
• [4] P. Grzeszczuk, E. R. Puczyłowski, On Goldie and dual Goldie dimensions, J. Pure Appl. Algebra 31 (1984), pp. 47–54.
• [5] P. Grzeszczuk, E. R. Puczyłowski, On infinite Goldie dimension of modular lattices and modules, J. Pure Appl. Algebra 35 (1985), pp. 151–155.
• [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.

Identyfikatory

DOI

10.18778/0138-0680.45.3.4.05