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
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