Splitting sets in integral domains
Authors:
D. D. Anderson and Muhammad Zafrullah
Journal:
Proc. Amer. Math. Soc. 129 (2001), 22092217
MSC (1991):
Primary 13A05, 13A15, 13G05
Published electronically:
December 28, 2000
MathSciNet review:
1823902
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: Let be an integral domain. A saturated multiplicatively closed subset of is a splitting set if each nonzero may be written as where and for all . We show that if is a splitting set in , then is a splitting set in , a multiplicatively closed subset of , and that is a splitting set in is an lcm splitting set of , i.e., is a splitting set of with the further property that is principal for all and . Several new characterizations and applications of splitting sets are given.
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Additional Information
D. D. Anderson
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
Email:
dananderson@uiowa.edu
Muhammad Zafrullah
Affiliation:
Department of Mathematics, SCEN 301, The University of Arkansas, Fayetteville, Arkansas 72701
Address at time of publication:
Department of Mathematics, Campus Box 8085, Idaho State University, Pocatello, Idaho 83209
Email:
kamla@compuserve.com, mzafrullah@usa.net
DOI:
http://dx.doi.org/10.1090/S0002993900058639
PII:
S 00029939(00)058639
Keywords:
Splitting sets
Received by editor(s):
May 5, 1999
Received by editor(s) in revised form:
December 18, 1999
Published electronically:
December 28, 2000
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2000
American Mathematical Society
