International Journal of Mathematics Trends and Technology
Volume 65 | Issue 8 | Year 2019 | Article Id. IJMTT-V65I8P501 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I8P501
The residue classes modulo 4 do not form a field and having the divisors of zero that will help us in showing the lattice suitably constructed is not distributive. The residue classes as considered as the entries of n * n matrix and the respective determinant is considered. M0 = [0 0 0 0], M1 = [ 0 0 0 1 ] ,..... , M255 = [3 3 3 3 ] ..........2.1 Considering the determinants of these matrices, it can be followed as the determinants vary from – 9 through 9. The set of matrices are partitioned into equivalence classes depending on the determinant and the partition is not regular. So, it is suitable to fit the structure into lattice and the 19 equivalence classes are having unequal number of members that are the n * n matrices. The equivalence classes and the respective number of members in each class are specified in the following chapter. The set of the equivalence classes form a lattice and is not distributive.
[1] Charles S. Peirce(1880), “On the Algebra of Logic”, American Journal of Mathematics
[2] Garrett Birkhoff(1967) Lattice Theory Colloquium Publications 25, American Mathematical Society
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T. SrinivasaRao , Dr. L. Sujatha, "Residue Matrix and not Distributive Lattice," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 8, pp. 1-3, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I8P501
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