caa a22 4500 445345160 CHVBK 20180317142826.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00233-011-9321-y doi (NATIONALLICENCE)springer-10.1007/s00233-011-9321-y Williams Kendall Department of Mathematics, Howard University, 20059, Washington, DC, USA aut Characterization of elements of polynomials in βS [Elektronische Daten] [Kendall Williams] Given the discrete space of natural numbers, we characterize the elements of polynomials evaluated on the points of βℕ. We establish these results by proving the characterization in a far more general setting. Let S be a discrete set which is a semigroup under two operations ⋅ and +. Let g(z 1,z 2, ,z k ) be any polynomial and p 1,p 2, ,p k be elements of βS. We provide a sufficient condition that a set A⊆S is a member of g(p 1,p 2, ,p k ) and use it to characterize the members of g(p 1,p 2, ,p k ) if each p i is an idempotent in (βS,+). Springer Science+Business Media, LLC, 2011 Stone-Čech compactification nationallicence Milliken-Taylor systems nationallicence Semigroup Forum Springer-Verlag 83/1(2011-08-01), 147-160 0037-1912 83:1<147 2011 83 233 https://doi.org/10.1007/s00233-011-9321-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00233-011-9321-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Williams Kendall Department of Mathematics, Howard University, 20059, Washington, DC, USA aut NATIONALLICENCE 773 0- Semigroup Forum Springer-Verlag 83/1(2011-08-01), 147-160 0037-1912 83:1<147 2011 83 233 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer