One sided ideals and Carlson's Theorem
Using left ideals, right ideals, and the smallest two sided ideal in a compact right topological semigroup, we derive an extension of the Main Lemma to Carlson's Theorem. This extension involves an infinite sequence of variable words over a finite alphabet, some of which are required to have the variable as the first letter and others of which are required to have the variable as the last letter.
Proceedings of the American Mathematical Society
Hindman, N., & McCutcheon, R. (2002). One sided ideals and Carlson's Theorem. Proceedings of the American Mathematical Society, 130 (9), 2559-2567. https://doi.org/10.1090/S0002-9939-02-06396-7