ACTA MATHEMATICA
UNIVERSITATIS COMENIANAE




Vol. LXXVII, 2 (2008)
p. 167 - 174

Distributive, standard and neutral elements in trellises

Shashirekha B. Rai

Received: May 24, 2006;   Revised: April 7, 2008;   Accepted: April 15, 2008



Abstract.   In this paper, the concepts of distributive, standard and neutral elements introduced in lattices by O. Ore, G. Grätzer and G. Birkhoff, respectively, have been extended to trellises (also called weakly associative lattices) and some of their analogous characterizations are obtained. Also, the concept of a normal trellis is introduced as a generalization of a lattice and it is proved that an element d of a normal trellis L is neutral if and only if for any x, y Î L, the elements d, x, y generate a distributive subtrellis of L.

Keywords:  pseudo-ordered set; trellis; distributive element; standard element; neutral element; normal trellis  

AMS Subject classification: Primary:  06B05;


PDF                               Compressed Postscript                                 Version to read







Acta Mathematica Universitatis Comenianae
ISSN 0862-9544   (Printed edition)

Faculty of Mathematics, Physics and Informatics
Comenius University
842 48 Bratislava, Slovak Republic  

Telephone: + 421-2-60295111 Fax: + 421-2-65425882  
e-Mail: amuc@fmph.uniba.sk    Internet: www.iam.fmph.uniba.sk/amuc
© 2008, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE