Not Distributive Lattice Over a Galois Field


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Authors

  • T. Srinivasarao Department of Mathematics, Adikavi Nannaya University, Rajamahendravaram, East Godavari, Andhra Pradesh, India
  • K. Geetha Lakshmi Department of Mathematics, Adikavi Nannaya University, Rajamahendravaram, East Godavari, Andhra Pradesh, India

Keywords:

Distributive Lattice, Galois Field, Euclidean ring

Abstract

A prime element in a Euclidean ring and to an irreducible polynomial in a polynomial ring defined over a field are identical. The irreducible polynomial allows us to construct a prime ideal which in turn leading to a maximal ideal. So, the maximal ideal and the Euclidean ring together form a quotient field in which the zero element is the maximal ideal itself. The quotient field is seen as the extended field over the field referred in the beginning. It is easily seen that the actual irreducible polynomial $f(x)$ is now reducible over the extended field. In the present case, we take a finite field and a polynomial from the polynomial ring over this field and verify the members of the field obey the distributive law or not. The purpose of producing a not distributive lattice is to see that enciphering can be done using the members of such a lattice in which it will be difficult to judge the correct deciphered text. Because, there will be multiple results in the deciphering approach. So, which is the correct decipher among the available cipher texts will be a matter of confusion. The present Galois field is over the field of residue classes modulo 3.

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Published

15-12-2019

How to Cite

T. Srinivasarao, & K. Geetha Lakshmi. (2019). Not Distributive Lattice Over a Galois Field. International Journal of Mathematics And Its Applications, 7(4), 123–125. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/213

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Section

Research Article