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Splitting sets in integral domains
Journal article   Open access   Peer reviewed

Splitting sets in integral domains

D. D Anderson and Muhammad Zafrullah
Proceedings of the American Mathematical Society, Vol.129(8), pp.2209-2217
2001
DOI: 10.1090/S0002-9939-00-05863-9
url
https://doi.org/10.1090/S0002-9939-00-05863-9View
Published (Version of record) Open Access

Abstract

Let D be an integral domain. A saturated multiplicatively closed subset S of D is a splitting set if each nonzero d E D may be written as d = sa where s E S and s'D n aD = s'aD for all s' E S. We show that if S is a splitting set in D, then SU(DN) is a splitting set in DN, N a multiplicatively closed subset of D, and that S C D is a splitting set in D[X] 4==> S is an lcm splitting set of D, i.e., S is a splitting set of D with the further property that sD n dD is principal for all s E S and d E D. Several new characterizations and applications of splitting sets are given.

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