Spectra of abelian wekly associative lattice groups

• Autorzy: Jiří Rachůnek
• Języki publikacji: EN

Abstrakty

EN

The notion of a weakly associative lattice group is a generalization of that of a lattice ordered group in which the identities of associativity of the lattice operations join and meet are replaced by the identities of weak associativity. In the paper, the spectral topologies on the sets of straightening ideals (and on some of their subsets) of abelian weakly associative lattice groups are introduced and studied.

Słowa kluczowe

EN

weakly associative lattice group; prime ideal; straightening ideal; spectral topology; spectrum

Kategorie tematyczne

• 06F15: Ordered groups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 51-61

Daty

wydano

2000

otrzymano

1998-05-21

poprawiono

1999-06-08

Twórcy

autor

Jiří Rachůnek

• Department of Algebra and Geometry, Palacký University, Tomkova 40, 779 00 Olomouc, Czech Republic

Bibliografia

• [1] M. R. Darnel, Theory of Lattice-Ordered Groups, Marcel Dekker, Inc., New York-Basel-Hong Kong 1995.
• [2] E. Fried, Tournaments and non-associative lattices, Ann. Univ. Sci. Budapest, Sect. Math. 13 (1970), 151-164.
• [3] E. Fried, A generalization of ordered algebraic systems, Acta Sci. Math. (Szeged) 31 (1970), 233-244.
• [4] A.M.W. Glass and W.Ch. Holland (Eds.), Lattice-Ordered Groups (Advances and Techniques), Kluwer Acad. Publ., Dordrecht-Boston-London 1989.
• [5] V.M. Kopytov and N.Ya. Medvedev, The Theory of Lattice Ordered Groups, Kluwer Acad. Publ., Dordrecht 1994.
• [6] J. Rachůnek, Structure spaces of lattice ordered groups, Czechoslovak Math. J. 39 (114) (1989), 686-691.
• [7] J. Rachůnek, Solid subgroups of weakly associative lattice groups, Acta Univ. Palack. Olom., Fac. Rer. Nat., no. 105, Math. 31 (1992), 13-24.
• [8] J. Rachůnek, On some varieties of weakly associative lattice groups, Czechoslovak Math. J. 46 (121) (1996), 231-240.
• [9] H. Skala, Trellis theory, Algebra Universalis 1 (1971), 218-233.
• [10] H. Skala, Trellis Theory, Memoirs Amer. Math. Soc., no. 121, Providence 1972.

Identyfikatory

DOI

10.7151/dmgaa.1005