Algebraic equivalents of flow disjointness
Robert Richmond Ellis, Shmuel Glasner, Leonard D. Shapiro · Illinois Journal of Mathematics · 1976
We discuss the implications of the techniques introduced in [2-1 for the theory of disjointness [3] of minimal transformation groups (called flows here).We were motivated by the question: (i) given flows X and Y with no common factor, under what conditions are they disjoint ?(I.e., when is X x Y minimal?)Since our techniques are algebraic in character, the question must be stated in terms of algebras rather than flows.This introduces the possibility of confusion since algebras correspond to pointed flows not to flows.Thus suppose that Z is a common factor of the flows X and Y.This means that there are epimor- phisms b: X --, Z and : Y Z.To translate this into the language of algebras we pick base points Xo X and Yo e Y with XoU Xo and you Yo (see Section for details).This allows us to correspond algebras .',M, c and to