p. 209 - 216 On ideals and congruence relations in trellises S. P. Bhatta and H. S. Ramananda Received: May 21, 2009; Revised: October 5, 2009; Accepted: November 27 21, 2009 Abstract. In this paper an attempt has been made to extend the ideal theory of lattices to trellises. Hashimoto's results concerning ideals and congruences in lattices are extended to trellises. Also a characterization of trellises in which every ideal is the kernel of at most one congruence relation is obtained by extending the corresponding well-known result in lattices due to Grätzer and Schmidt. Keywords: trellis; lattice; ideal lattice of a trellis; congruence relation. AMS Subject classification: Primary: 06B05, 06B10 PDF Compressed Postscript Version to read 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 © 2010, ACTA MATHEMATICA UNIVERSITATIS COMENIANAE |