eng Ansari Education and Research Society Journal of Ultra Scientist of Physical Sciences August, 2017 29 8 352 357 http://dx.doi.org/10.22147/jusps-A/290807 839 article R. RATHA JEYALAKSHMI (rathajeyal@yahoo.com) 1 Department of Mathematics Mepco Schlenk Engineering College, Sivakasi u2013 626005 Tamilnadu (India) <p style="text-align: justify;">In this paper we use the Hall &ndash; Dilworth gluing construction to obtain multiple congruences of a lattice L. For any finite lattice L, ( , ) m n G L B , the gluing of L and n B over F and I, both F and I are isomorphic to 2 C . For any lattice L, the congruences of Gm (L, Bn ) is 2(n1) times the congruences of L where F be the filter of L and I be an ideal of n B and are isomorphic to 2 C . We call ( , ) m n G L B the congruence multiple operator.</p> https://www.ultrascientist.org/paper/839/ Gluing, filter ideal congruence multiple congruence Mathematics Subject classification: Primary: 06B10 Secondary: 06D05