Double coset algebras

The Iwahori-Hecke algebra H(M,G) corresponding to a finite monoid M and subgroup G is isomorphic to the double coset algebra A(M,G) where G={G} consists of a single set. So, as a special case of our result, we obtain Z-forms LGS(M,G) and RGS(M,G) for arbitrary Iwahori-Hecke algebras. The existence of a Z-form for any such H(M,G) appears to be a new result.