Paper Title
Rank of Semi Group: Generating Sets and Independent

Abstract
We investigate a certain characterisation for rank of a semigroup by Howie and Ribeiro (1999), to ascertain the relevance of the concept of independence. There are cases where the concept of independence fails to be useful for this purpose. One would expect the basis element to be the maximal independent subset of a given semigroup. However, we construct examples for semigroups - finite and infinite, commutative and non-commutative, where there exists finite basis and the number of independent elements is larger than the basis. Index Terms - Generating sets, Independent Set, Rank, Cyclic Semigroup, Basis, Commutative