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

Let S be a semigroup with a left multiplier on S. A new product on S is defined by related to S and such that S and the new semigroup ST have the same underlying set as S. It is shown that if is injective then where، is the extension of on Also، we show that if is bijective then is amenable if and only if is so. Moreover، if S completely regular، then is weakly amenable.