Distributivity of bounded lattices with sectionally antitone involutions

Ivan Chajda

Discussiones Mathematicae - General Algebra and Applications (2005)

  • Volume: 25, Issue: 2, page 155-163
  • ISSN: 1509-9415

Abstract

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We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.

How to cite

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Ivan Chajda. "Distributivity of bounded lattices with sectionally antitone involutions." Discussiones Mathematicae - General Algebra and Applications 25.2 (2005): 155-163. <http://eudml.org/doc/287653>.

@article{IvanChajda2005,
abstract = {We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.},
author = {Ivan Chajda},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {sectionally antitone involution; bounded lattice; distributive lattice; MV-algebra; lattices; antitone involutions; MV-algebras},
language = {eng},
number = {2},
pages = {155-163},
title = {Distributivity of bounded lattices with sectionally antitone involutions},
url = {http://eudml.org/doc/287653},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Ivan Chajda
TI - Distributivity of bounded lattices with sectionally antitone involutions
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2005
VL - 25
IS - 2
SP - 155
EP - 163
AB - We present a simple condition under which a bounded lattice L with sectionally antitone involutions becomes an MV-algebra. In thiscase, L is distributive. However, we get a criterion characterizingdistributivity of L in terms of antitone involutions only.
LA - eng
KW - sectionally antitone involution; bounded lattice; distributive lattice; MV-algebra; lattices; antitone involutions; MV-algebras
UR - http://eudml.org/doc/287653
ER -

References

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  1. [1] J.C. Abbott, Semi-boolean algebra, Matem. Vestnik 4 (1967), 177-198. Zbl0153.02704
  2. [2] R.L.O. Cignoli, I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-valued Reasoning, Kluwer, Dordrecht/Boston/London 2000. Zbl0937.06009
  3. [3] I. Chajda, Lattices and semilattices having an antitone involution inevery upper interval, Comment. Math. Univ. Carol (CMUC) 44 (4) (2003), 577-585. Zbl1101.06003
  4. [4] I. Chajda and P. Emanovský, Bounded lattices with antitone involutions and properties of MV-algebras, Discuss. Math. General Algebra and Appl. 24 (2004), 31-42. Zbl1082.03055
  5. [5] I. Chajda, R. Halas and J. Kühr, Distributive lattices with sectionally antitone involutions, Acta Sci. Math. (Szeged), to appear. Zbl1099.06006

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