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Mathematics (HMC)

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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.


Dedicated to the memory of Zdenek Frolik.

Previously linked to as:,444.

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