Starting from a nonempty set X and a commutative semigroup G acting on X we construct a new space B(X,G) whose algebraic character is similar to a quotient field. The construction of the quotient field from an integral domain is a special case of our construction. Other interpretations of the construction include the space of Schwartz distributions of finite order, tempered distributions, Radon measures, and Boehmians.
In this paper we describe the construction of B(X,G), discuss some general properties of B(X,G), and present some applications of the construction.
"GENERALIZED QUOTIENTS WITH APPLICATIONS IN ANALYSIS." Methods Appl. Anal. 10 (3) 377 - 386, Sept 2003.