Some properties of Eulerian lattices

R. Subbarayan; A. Vethamanickam

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 4, page 499-507
  • ISSN: 0010-2628

Abstract

top
In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.

How to cite

top

Subbarayan, R., and Vethamanickam, A.. "Some properties of Eulerian lattices." Commentationes Mathematicae Universitatis Carolinae 55.4 (2014): 499-507. <http://eudml.org/doc/262003>.

@article{Subbarayan2014,
abstract = {In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.},
author = {Subbarayan, R., Vethamanickam, A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Eulerian lattices; 0-distributive lattices; pseudo-0-distributive lattices; super-0-distributive lattices; Eulerian lattices; Boolean lattices; maximal chains; Möbius functions; posets; 0-distributive lattices},
language = {eng},
number = {4},
pages = {499-507},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some properties of Eulerian lattices},
url = {http://eudml.org/doc/262003},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Subbarayan, R.
AU - Vethamanickam, A.
TI - Some properties of Eulerian lattices
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 4
SP - 499
EP - 507
AB - In this paper, we prove that Eulerian lattices satisfying some weaker conditions for lattices or some weaker conditions for 0-distributive lattices become Boolean.
LA - eng
KW - Eulerian lattices; 0-distributive lattices; pseudo-0-distributive lattices; super-0-distributive lattices; Eulerian lattices; Boolean lattices; maximal chains; Möbius functions; posets; 0-distributive lattices
UR - http://eudml.org/doc/262003
ER -

References

top
  1. Balasubramani P., Stone topologies of the set of prime filters of a 0 -distributive lattice, Indian J. Pure Appl. Math. 35 (2004), no. 2, 149–158. MR2040729
  2. Bayer M., Billera J., 10.1090/conm/034/777703, Contemporary Mathematics 34 (1984), 207-252. DOI10.1090/conm/034/777703
  3. Chajda I., Radeleczki S., 0 -conditions and tolerance schemes, Acta Math. Univ. Comenian. 72 (2003), no. 2, 177–184. Zbl1087.08002MR2040261
  4. Crawley P., Dilworth R.P., Algebraic Theory of Lattices, Prentice-Hall, Inc., Englewod. Cliffs, New Jersey, 1973. Zbl0494.06001
  5. Davey B.A., Priestley H.A., Introduction to Lattices and Order, Second Edition, Cambridge University Press, Cambridge, 2002. Zbl1002.06001MR1902334
  6. Gragg K.M., Kung J.P.S., 10.1016/0097-3165(92)90006-G, J. Combin. Theory Ser. A 60 (1992), 246–263. Zbl0822.06007MR1168156DOI10.1016/0097-3165(92)90006-G
  7. Grätzer G., General Lattice Theory, Birkhäuser, Basel, 1978. MR0504338
  8. Grünbaum B., Convex Polytopes, Interscience, London-New York, 1967. Zbl1033.52001MR0226496
  9. Pawar Y.S., 0 - 1 -distributive lattices, Indian J. Pure Appl. Math. 24 (1993), no. 3, 173–178. Zbl0765.06015MR1210389
  10. Mckenzie R.N., Mcnulty G.E., Tayler W.F., Algebras, Lattices, Varieties, Vol I, Wardswoth and Brooks/Cole, Monterey, California, 1987. 
  11. Rota G.C., 10.1007/BF00531932, Z. Wahrschainlichkeitstheorie und Verw. Gebiete 2 (1964), 340-368. Zbl0121.02406MR0174487DOI10.1007/BF00531932
  12. Santhi V. K., Topics in Commutative Algebra, Ph.D. thesis, Madurai Kamaraj University, 1992. 
  13. Subbarayan R., Lattice Theory, Ph.D thesis, Bharathidasan University, 2008. 
  14. Stanley R.P., 10.1016/0097-3165(82)90017-6, J. Combin. Theory Ser. A 32 (1982), 131–161. Zbl0496.06001MR0654618DOI10.1016/0097-3165(82)90017-6
  15. Stanley R.P., 10.1007/978-1-4615-9763-6, Wordsworth and Brooks/Cole, Monterey, CA, 1986. Zbl1247.05003DOI10.1007/978-1-4615-9763-6
  16. Stanley R.P., Supersolvable lattices, Algebra Universalis 4 (1974), 361–371. Zbl0256.06002MR0354473
  17. Varlet J.C., A generalization of the notion of pseudo-complimentedness, Bull. Soc. Roy. Sci. Liège, 37 (1968), 149–158. MR0228390
  18. Vethamanickam A., Topics in Universal Algebra, Ph.D. thesis, Madurai Kamaraj University, 1994. 
  19. Vethamanickam A., Subbarayan R., Some simple extensions of Eulerian lattices, Acta Math. Univ. Comenianae 79 (2010), no. 1, 47–54. Zbl1212.06007MR2684207
  20. Walendziak A., On consistent lattices, Acta Sci. Math. (Szeged) 59 (1994), 49–52. Zbl0803.06006MR1285428

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.