• DocumentCode
    3266876
  • Title

    Algebraic properties of totally irreducible elements of clone lattices

  • Author

    Pogosyan, G.R.

  • Author_Institution
    Math. & Comput. Sci., Int. Christian Univ., Tokyo, Japan
  • fYear
    2004
  • fDate
    19-22 May 2004
  • Firstpage
    109
  • Lastpage
    114
  • Abstract
    Totally join- (meet-) irreducible elements are important for algebraic lattices since the join-(meet-) generates them. We study such elements for clone lattices, particularly for the clone lattice on a k-element universe. We show that in this case the set of totally join- (meet-) irreducible clones is countable; in particular that there are 2k-1(2k-2) countable descending chains of such clones.
  • Keywords
    algebra; algebraic lattices; clone lattice algebraic properties; clone lattice totally irreducible elements; countable clone set; countable descending clone chains; join-irreducible elements; k-element universe; meet-irreducible elements; Algebra; Cloning; Computer science; Lattices; Logic; Mathematics; Statistics;
  • fLanguage
    English
  • Publisher
    ieee
  • Conference_Titel
    Multiple-Valued Logic, 2004. Proceedings. 34th International Symposium on
  • ISSN
    0195-623X
  • Print_ISBN
    0-7695-2130-4
  • Type

    conf

  • DOI
    10.1109/ISMVL.2004.1319928
  • Filename
    1319928
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=3266876