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The Direct Decomposition of l-algebras into Products of Subdirectly Irreducible Factors

Part of: Lattices Ordered structures Algebraic structures

Published online by Cambridge University Press:  09 April 2009

Sándor Radeleczki
Sándor Radeleczki
Affiliation:
Institute of Mathematics University of Miskolc-Egyetemváros3515 MiskoicHungary e-mail: [email protected]
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Abstract

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Generalizing earlier results of Katriňák, El-Assar and the present author we prove new structure theorems for l-algebras. We obtain necessary and sufficient conditions for the decomposition of an arbitrary bounded lattice into a direct product of (finitely) subdirectly irreducible lattices.

MSC classification

Secondary: 08A05: Structure theory 06F99: None of the above, but in this section 06B05: Structure theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 75 , Issue 1 , August 2003 , pp. 41 - 56
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Burris, S. and Sankappanavar, H. P., A course in universal algebra (Springer, New York, 1981).CrossRefGoogle Scholar
[2]Dilworth, R. P., ‘The structure of relatively complemented lattices’, Ann. of Math. 51(1950), 348–359.CrossRefGoogle Scholar
[3]Frink, O., ‘Pseudo-complements in semi-lattices’, Duke Math. J. 29 (1962), 505–514.CrossRefGoogle Scholar
[4]Grätzer, G., General lattice theory (Academic Press, New York, 1978).CrossRefGoogle Scholar
[5]Janowitz, M. F., ‘Section semicomplemented lattices’, Math. Z. 108 (1968), 63–76.CrossRefGoogle Scholar
[6]Janowitz, M. F., ‘Complemented congruences on complemented lattices’, Pacific J. Math. 73 (1977), 87–90.CrossRefGoogle Scholar
[7]Katriňák, T., ‘Notes on Stone lattices II’, Mat. Fyz. Časop. SAV 17 (1967), 20–37 (In Russian).Google Scholar
[8]Katriňák, T. and El-Assar, S., ‘Algebras with Boolean and Stonean congruence lattices’, Acta Math. Hungar. 48 (1986), 301–316.CrossRefGoogle Scholar
[9]Libkin, L., ‘Direct decomposition of atomistic algebraic lattices’, Algebra Universalis 33 (1995), 127–135.CrossRefGoogle Scholar
[10]Maeda, F. and Maeda, S., Theory of symmetric lattices (Springer, Berlin, 1970).CrossRefGoogle Scholar
[11]Radeleczki, S., ‘Maeda-type decomposition of CJ-generated algebraic lattices’, South East Asian Bull. Math. 25 (2001), 503–513.CrossRefGoogle Scholar