Ordered Ultraconnected Rings

Authors

Melvin Henriksen, Harvey Mudd CollegeFollow
Frank A. Smith, Kent State UniversityFollow

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.

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

Rights Information

© 1990 Charles University in Prague

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

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