Splitting sets in integral domains

Authors:
D. D. Anderson and Muhammad Zafrullah

Journal:
Proc. Amer. Math. Soc. **129** (2001), 2209-2217

MSC (1991):
Primary 13A05, 13A15, 13G05

DOI:
https://doi.org/10.1090/S0002-9939-00-05863-9

Published electronically:
December 28, 2000

MathSciNet review:
1823902

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
dan-anderson@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:
https://doi.org/10.1090/S0002-9939-00-05863-9

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