Spectra of abelian wekly associative lattice groups

Jiří Rachůnek

Discussiones Mathematicae - General Algebra and Applications (2000)

  • Volume: 20, Issue: 1, page 51-61
  • ISSN: 1509-9415

Abstract

top
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.

How to cite

top

Jiří Rachůnek. "Spectra of abelian wekly associative lattice groups." Discussiones Mathematicae - General Algebra and Applications 20.1 (2000): 51-61. <http://eudml.org/doc/287715>.

@article{JiříRachůnek2000,
abstract = {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.},
author = {Jiří Rachůnek},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {weakly associative lattice group; prime ideal; straightening ideal; spectral topology; spectrum},
language = {eng},
number = {1},
pages = {51-61},
title = {Spectra of abelian wekly associative lattice groups},
url = {http://eudml.org/doc/287715},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Jiří Rachůnek
TI - Spectra of abelian wekly associative lattice groups
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2000
VL - 20
IS - 1
SP - 51
EP - 61
AB - 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.
LA - eng
KW - weakly associative lattice group; prime ideal; straightening ideal; spectral topology; spectrum
UR - http://eudml.org/doc/287715
ER -

References

top
  1. [1] M. R. Darnel, Theory of Lattice-Ordered Groups, Marcel Dekker, Inc., New York-Basel-Hong Kong 1995. Zbl0810.06016
  2. [2] E. Fried, Tournaments and non-associative lattices, Ann. Univ. Sci. Budapest, Sect. Math. 13 (1970), 151-164. Zbl0224.06004
  3. [3] E. Fried, A generalization of ordered algebraic systems, Acta Sci. Math. (Szeged) 31 (1970), 233-244. Zbl0226.06005
  4. [4] A.M.W. Glass and W.Ch. Holland (Eds.), Lattice-Ordered Groups (Advances and Techniques), Kluwer Acad. Publ., Dordrecht-Boston-London 1989. Zbl0705.06001
  5. [5] V.M. Kopytov and N.Ya. Medvedev, The Theory of Lattice Ordered Groups, Kluwer Acad. Publ., Dordrecht 1994. Zbl0834.06015
  6. [6] J. Rachůnek, Structure spaces of lattice ordered groups, Czechoslovak Math. J. 39 (114) (1989), 686-691. Zbl0703.06010
  7. [7] J. Rachůnek, Solid subgroups of weakly associative lattice groups, Acta Univ. Palack. Olom., Fac. Rer. Nat., no. 105, Math. 31 (1992), 13-24. Zbl0776.06016
  8. [8] J. Rachůnek, On some varieties of weakly associative lattice groups, Czechoslovak Math. J. 46 (121) (1996), 231-240. Zbl0870.06016
  9. [9] H. Skala, Trellis theory, Algebra Universalis 1 (1971), 218-233. Zbl0242.06003
  10. [10] H. Skala, Trellis Theory, Memoirs Amer. Math. Soc., no. 121, Providence 1972. Zbl0242.06004

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.