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FACTORIZATION IN PRÜFER DOMAINS

Part of: Arithmetic rings and other special rings General commutative ring theory

Published online by Cambridge University Press:  30 October 2017

JIM COYKENDALL  and
RICHARD ERWIN HASENAUER
JIM COYKENDALL
Affiliation:
Clemson University, Clemson, SC 29634, USA e-mail: [email protected]
RICHARD ERWIN HASENAUER
Affiliation:
Northeastern State University, Tahlequah, OK 74464, USA e-mail: [email protected]
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Abstract

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We construct a norm on the nonzero elements of a Prüfer domain and extend this concept to the set of ideals of a Prüfer domain. These norms are used to study factorization properties Prüfer of domains.

MSC classification

Primary: 13A50: Actions of groups on commutative rings; invariant theory
Secondary: 13F15: Rings defined by factorization properties (e.g., atomic, factorial, half-factorial)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 2 , May 2018 , pp. 401 - 409
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. Anderson, D. F. and El Abidine, D. N., Factorization in integral domains III, J. Pure Appl. Algebra 135 (2) (1999), 107–127. MR 1667552CrossRefGoogle Scholar
2. Anderson, D. D., Anderson, D. F. and Zafrullah, M., Factorization in integral domains II, J. Algebra 152 (1992), 78–93.CrossRefGoogle Scholar
3. Anderson, D. D., Anderson, D. F. and Zafrullah, M., Factorization in integral domains, J. Pure Appl. Algebra 69 (1990), 1–19.CrossRefGoogle Scholar
4. Bazzoni, S., Groups in the class semigroup of a Prüfer domain of finite character, Comm. Algebra 28 (11) (2000), 5157–5167. MR 1785492CrossRefGoogle Scholar
5. Dumitrescu, T. and Zafrullah, M., Characterizing domains of finite *-character, J. Pure Appl. Algebra 214 (11) (2010), 2087–2091. MR 2645341CrossRefGoogle Scholar
6. Fontana, M., Houston, E. and Lucas, T., Factoring ideals in Prüfer domains, J. Pure Appl. Algebra 211 (1) (2007), 1–13. MR 2333758CrossRefGoogle Scholar
7. Fuchs, L., Partially ordered algebraic systems (Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963). MR 0171864Google Scholar
8. Fuchs, L. and Mosteig, E., Ideal theory in Prüfer domains–an unconventional approach, J. Algebra 252 (2) (2002), 411–430. MR 1925145CrossRefGoogle Scholar
9. Gilmer, Robert, Multiplicative ideal theory, Queen's Papers in Pure and Applied Mathematics, vol. 90 (Queen's University, Kingston, ON, 1992), Corrected reprint of the 1972 edition. MR 1204267Google Scholar
10. Gonshor, H., An introduction to the theory of surreal numbers, London Mathematical Society Lecture Note Series, vol. 110 (Cambridge University Press, Cambridge, 1986). MR 872856CrossRefGoogle Scholar
11. Grams, A., Atomic rings and the ascending chain condition for principal ideals, Proc. Cambridge Philos. Soc. 75 (1974), 321–329. MR 0340249CrossRefGoogle Scholar
12. Hasenauer, R. E., Normsets of almost Dedekind domains and atomicity, J. Commut. Algebra 8 (1) (2016), 61–75. MR 3482346CrossRefGoogle Scholar
13. Alan Loper, K. and Lucas, T. G., Factoring ideals in almost Dedekind domains, J. Reine Angew. Math. 565 (2003), 61–78. MR 2024646Google Scholar
14. Ohm, J., Some counterexamples related to integral closure in D[[x]], Trans. Amer. Math. Soc. 122 (1966), 321–333. MR 0202753Google Scholar
15. Olberding, B., Factorization into radical ideals, Arithmetical properties of commutative rings and monoids, Lect. Notes Pure Appl. Math., vol. 241 (Chapman & Hall/CRC, Boca Raton, FL, 2005), 363–377. MR 2140708Google Scholar