Sums equal to products in βN

Baker, J., and R. Butcher,The Stone-Čech compactification of a topological semigroup, Math. Proc. Cambr. Phil. Soc. 80 (1976), 103–107. Baker, J., and P. Milnes,The ideal structure of the Stone-Čech compactification of a group, Math. Proc. Cambr. Phil. Soc. 82 (1977), 401–409. Berglund, J., and K.H. Hofmann,Compact semitopological semigroups and weakly almost periodic functions, Lecture Notes in Math. 42, Springer-Verlag, Berlin, (1967). Berglund, J., H. Junghenn, and P. Milnes,Compact right topological semigroups and generalizations of almost periodicity, Lecture Notes in Math. 663, Springer-Verlag, Berlin, (1978). Brown, G., and W. Moran,Idempotents of compact monothetic semigroups, Proc. London Math. Soc. 22 (1971), 211–221. Butcher, R.,The Stone-Čech compactification of a topological semigroup,and its algebra of measures, Dissertation, University of Sheffield, (1975). Chou, C.,On a geometric property of the set of invariant means on a group, Proc. Amer. Math. Soc. 30 (1971), 296–302. Comfort, W.,Ultrafilters—some old and some new results, Bull. Amer. Math. Soc. 83 (1977), 417–455. van Douwen, E.,The Čech-Stone compactification of a discrete cancellative groupoid, Manuscript. Dunkl, C., and D. Ramirez,Representations of commutative semigroups, Lecture Notes in Math. 435, Springer-Verlag, Berlin, (1975). Gillman, L., and M. Jerison,Rings of continuous functions, van Nostrand, Princeton, (1960). Hausdorff, F.,Über Zwei Sätze von G. Fichtenholz and L. Kantorovitch, Studia Math. 6 (1936), 18–19. Hindman, N.,Partitions and sums and products of integers, Trans. Amer. Math. Soc. 247 (1979), 227–245. —,Simultaneous idempotents in βN/Nand finite sums and products in N, Proc. Amer. Math. Soc., 77 (1979), 150–154. —,Ultrafilters and combinatorial number theory, Lecture Notes in Math. 751, Springer-Verlag, Berlin, (1979), 119–184. Macri, N.,The continuity of the Arens product on the Stone-Čech compactification of semigroups, Trans. Amer. Math. Soc. 191 (1974), 185–193. Namukura, K.,On bicompact semigroups, Math J. Okayama Univ. 1 (1952), 99–108. Ruppert, W.,Rechtstopologische Halbgruppen, J. Rein Angew. Math., 261 (1973), 123–133.