#### Document Type

Article

#### Department

Mathematics (HMC)

#### Publication Date

1990

#### Abstract

A ring R with identity element 1 is called ultraconnected if for each unital homomorphism ϕ of Z^{ω }into R, there is an i < ω such that ϕ(*f*) = *f*(i) • 1 for every *f* € Z^{ω }. 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 Z^{ω}/P for some free minimal prime ideal P of Z^{ω}.

#### Rights Information

© 1990 Charles University in Prague

#### Terms of Use & License Information

#### Recommended Citation

Henriksen, M., and F. A. Smith. "Ordered ultraconnected rings." Commentationes Mathematicae Universitatis Carolinae 31.1 (1990): 41-47.

## Comments

Dedicated to the memory of Zdenek Frolik.

Previously linked to as: http://ccdl.libraries.claremont.edu/u?/irw,444.

Article can also be found at http://dml.cz/dmlcz/106818