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Bounds On Element Order In Rings Z(M) With Divisors Of Zero, C. H. Cooke
Bounds On Element Order In Rings Z(M) With Divisors Of Zero, C. H. Cooke
Mathematics & Statistics Faculty Publications
If p is a prime, integer ring Zp has exactly ¢¢(p) generating elements ω, each of which has maximal index Ip(ω) = (p) = p − 1. But, if m = ΠRJ = 1pαJJ is composite, it is possible that Zm does not possess a generating element, and the maximal index of an element is not easily discernible. Here, it is determined when, in the absence of a generating element, one can still with confidence place bounds on the maximal index. Such a bound is usually less than ¢(m …