| dc.contributor.author | Staruch, Bogdan | |
| dc.date.accessioned | 2017-07-10T12:08:39Z | |
| dc.date.available | 2017-07-10T12:08:39Z | |
| dc.date.issued | 2016 | |
| dc.identifier.issn | 0138-0680 | |
| dc.identifier.uri | http://hdl.handle.net/11089/22187 | |
| dc.description.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. | 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 | uniform lattice | en_GB |
| dc.subject | dimension of algebra | en_GB |
| dc.subject | one-dimensional algebra | en_GB |
| dc.subject | subdirect product | en_GB |
| dc.subject | star-product | en_GB |
| dc.subject | decomposition of algebra | en_GB |
| dc.title | Irredundant Decomposition of Algebras into One-Dimensional Factors | 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 | [213]-238 | |
| dc.contributor.authorAffiliation | University of Warmia and Mazury, Olsztyn, Department of Mathematics and Computer Science | |
| dc.identifier.eissn | 2449-836X | |
| dc.references | G. Birkhoff, On the structure of abstract algebras, Proc. Cambridge Philos. Soc. 31 (1935), pp. 433–454. | en_GB |
| dc.references | G. Birkhoff, Lattice Theory. American Mathematical Society Colloquium Publications, vol. 25, American Mathematical Society, New York, (1948). | en_GB |
| 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 | G. Grätzer, E. T. Schmidt, Characterizations of congruence lattices of abstract algebras, Acta Sci. Math. (Szeged) 24(1963), pp. 34-59. | en_GB |
| dc.references | P. Grzeszczuk, J. Okniński, E. R. Puczyłowski, Relations between some dimensions of modular lattices, Comm. Algebra 17(1989), pp. 1723–1737. | 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 infnite Goldie dimension of modular lattices and modules, J. Pure Appl. Algebra 35(1985), pp. 151–155. | en_GB |
| dc.references | T. Katrinák, S. El-Assar, Algebras with Boolean and Stonean congruence lattices, Acta Math. Hungar. 48 (1986), pp. 301–31. | 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 | J. Krempa, B. Terlikowska-Osłowska, On uniform dimension of lattices, Contributions to General Algebra 9, Holder-Pichler-Tempsky, Wien, 1995, pp. 219–230. | en_GB |
| dc.references | R. N. McKenzie, G. F. McNulty, W. F. Taylor, Algebras, Lattices, Varieties, Vol. 1, The Wadsworth Brooks/Cole Mathematics Series. Wadsworth Brooks/Cole Advanced Books Software, Monterey, California, (1987). | 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 | S. Roman, Lattices and Ordered Sets, Springer-Verlag, New York, 2008. | en_GB |
| dc.references | A. Walendziak, On direct decompositions of lattices, bf Algebra Universalis, 37 (1997), pp. 185–190. | en_GB |
| dc.references | A. Walendziak, Decompositions in lattices and some representations of algebras, Dissertationes Mathematicae 392, (2001). | 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.references | A. P. Zolotarev, Direct decompositions of elements, and Goldie numbers in balanced lattices, Russian Math. (Iz. VUZ), 36:10 (1992), pp. 19-27. | en_GB |
| dc.contributor.authorEmail | bstar@uwm.edu.pl | |
| dc.identifier.doi | 10.18778/0138-0680.45.3.4.06 | |
| dc.relation.volume | 45 | en_GB |
