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Green’s Equivalence Relations on the multiplicative semigroup zn

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The Multiplicative Semigroup Zn has a vital role in the studies of computer scientists. This paper present the various characteristics of this structure. The rank of Zn, the characteristics of regular Zn, the idempotents in Zn, Green’s relations on Zn and the D-classes of Zn are the topics under discussion. It is already known that the Multiplicative semigroup Zn is regular iff n is square free. This paper is expected to be helpful for a comparative study between regular and non-regular Zn.

Keywords:Multiplicative semigroup integers modulo n, rank of a semigroup, regular semigroup, idempotent elements of a semigroup, Euler function, Green’s relations, Green’s equivalence classes.


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