Some applications of MV algebras

Abstract

In this paper, some properties and applications of MV-algebras are provided. We define a Fibonacci sequence in an MV-algebra and we prove that such a stationary sequence gives us an idempotent element. Taking into account of the representation of a finite MV-agebra, by using Boolean elements of this algebra, we prove that such a sequence is always stationary and is not periodic as in the situation when such a sequence is studied on the group (Zn; +), the group of integers modulo n. Moreover, as an application in Coding Theory, to a Boolean algebra is attached a binary block code and is proved that, under some conditions, the converse is also true.