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Let S be a semigroup and be a left multiplier on S. We present a general method of defining a new product on S which makes S a semigroup. Let denote S with the new product. These two semigroups are sometims different and we try to find conditions on S and such that the semigroups S and have the same properties. This idea has started by Birtel in [1] for Banach algebras and continued by Larsen in [11]. Recently, this notion developed by some authors, for more details see , [10], , [12] and [15]. One of the best result in this work expresses that is Arens regular if and only if is a compact group [10]. We continue this direction on the regularity of S and and the amenability of their semigroup algebras. The term of semigroup will be a non-empty set S endowed with an associative binary operation on , defined by . If S is also a Hausdorff topological space and the binary operation is jointly continuous, then S is called a topological semigroup.

Amenability and Weak Amenability of the Semigroup Algebra l^1 (〖 S〗_T )