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Convex Directed Subgroups of a Group of Divisibility

Published online by Cambridge University Press:  20 November 2018

Joe L. Mott
Joe L. Mott*
Affiliation:
Florida State University, Tallahassee, Florida
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If D is an integral domain with quotient field K, the group of divisibility G(D) of D is the partially ordered group of non-zero principal fractional ideals with aD ≦ bD if and only if aD contains bD. If K* denotes the multiplicative group of K and U(D) the group of units of D, then G(D) is order isomorphic to K*/U(D), where aU(D) ≦ bU(D) if and only if b/a ∊ D.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 3 , June 1974 , pp. 532 - 542
Copyright
Copyright © Canadian Mathematical Society 1974

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