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Howie and Ribeiro \cite{a.Howie99,a.Howie00} introduced various ranks, viz.small rank, lower rank, intermediate rank, upper rank and the large rank of afinite semigroup. In this note, we investigate all these ranks of the semigroupof endomorphisms over Brandt semigroup.

Rank Properties of the Semigroup of Endomorphisms over Brandt semigroup