A ring R with identity element 1 is called ultraconnected if for each unital homomorphism ϕ of Zω into R, there is an i < ω such that ϕ(f) = f(i) • 1 for every f € Zω . Our main result is that if no sum of nonzero squares in R is 0 and R has only trivial idempotents, then R fails to be ultraconnected iff R contains a subring isomorphic to Zω/P for some free minimal prime ideal P of Zω.
© 1990 Charles University in Prague
Henriksen, M., and F. A. Smith. "Ordered ultraconnected rings." Commentationes Mathematicae Universitatis Carolinae 31.1 (1990): 41-47.