Boundary map and overrings of half-factorial domains

Nathalie Gonzalez; Sébastien Pellerin

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 1, page 173-185
  • ISSN: 0392-4033

Abstract

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We investigate factorization of elements in overrings of a half-factorial domain A in relation with the behaviour of the boundary map of A . It turns out that a condition, called C , on the extension plays a central role in this study. We finally apply our results to the special case of A + X B X polynomial rings.

How to cite

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Gonzalez, Nathalie, and Pellerin, Sébastien. "Boundary map and overrings of half-factorial domains." Bollettino dell'Unione Matematica Italiana 8-B.1 (2005): 173-185. <http://eudml.org/doc/196178>.

@article{Gonzalez2005,
abstract = {We investigate factorization of elements in overrings of a half-factorial domain $A$ in relation with the behaviour of the boundary map of $A$. It turns out that a condition, called $\mathcal\{C\}^\{\star\}$, on the extension plays a central role in this study. We finally apply our results to the special case of $A+XB[X]$ polynomial rings.},
author = {Gonzalez, Nathalie, Pellerin, Sébastien},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {173-185},
publisher = {Unione Matematica Italiana},
title = {Boundary map and overrings of half-factorial domains},
url = {http://eudml.org/doc/196178},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Gonzalez, Nathalie
AU - Pellerin, Sébastien
TI - Boundary map and overrings of half-factorial domains
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/2//
PB - Unione Matematica Italiana
VL - 8-B
IS - 1
SP - 173
EP - 185
AB - We investigate factorization of elements in overrings of a half-factorial domain $A$ in relation with the behaviour of the boundary map of $A$. It turns out that a condition, called $\mathcal{C}^{\star}$, on the extension plays a central role in this study. We finally apply our results to the special case of $A+XB[X]$ polynomial rings.
LA - eng
UR - http://eudml.org/doc/196178
ER -

References

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  1. ANDERSON, D. F. - CHAPMAN, S. T. - SMITH, W. W., Overrings of half-factorial domains, Canad. Math. Bull., 37 (1994), 437-442. Zbl0815.13001MR1303668
  2. ANDERSON, D. F. - PARK, J., Locally half-factorial domains, Houston J. Math., 23 (1997), 617-630. Zbl0922.13015MR1687334
  3. ANDERSON, D. F. - PARK, J., Factorization in subrings of K X and K X , Lecture Notes in Pure and Applied Mathematics, vol. 189, Marcel Dekker, New York, 1997, 227-241. Zbl0902.13014MR1460775
  4. CARLITZ, L., A characterization of algebraic number fields with class number two, Proc. Amer. Math. Soc., 11 (1960), 391-392. Zbl0202.33101MR111741
  5. CHAPMAN, S. T. - COYKENDALL, J., Half-factorial domains, a survey, in Non-Noetherian Commutative Ring Theory, Kluwer Academic Publishers, 2001. Zbl0987.13010MR1858159
  6. CHAPMAN, S. T. - GLAZ, S., One hundred problems in commutative ring theory, in Non-Noetherian Commutative Ring Theory, Kluwer Academic Publishers, 2001. Zbl0979.13001MR1858175
  7. CHAPMAN, S. T. - SMITH, W. W., Factorization in Dedekind domains with finite class group, Israel J. Math, 71 (1990), 65-95. Zbl0717.13014MR1074505
  8. COYKENDALL, J., A characterization of polynomial rings with the half-factorial property, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, 189 (1997), 291-294. Zbl0886.13010MR1460780
  9. COYKENDALL, J., The half-factorial property in integral extensions, Comm. Algebra, 27 (7) (1999), 3153-3159. Zbl0956.13005MR1695319
  10. COYKENDALL, J., Half-factorial domains in quadratic fields, J. Algebra, 235 (2001), 417-430. Zbl0989.11058MR1805465
  11. COYKENDALL, J., On the integral closure of a half-factorial domain, J. Pure Appl. Algebra, 180 (2003), 25-34. Zbl1031.13011MR1966521
  12. GONZALEZ, N., Elasticity of A + X B X domains, J. Pure Appl. Algebra, 138 (1999), 119-137. Zbl0935.13002MR1689617
  13. [13] GONZALEZ, N. - PELLERIN, S. - ROBERT, R., Elasticity of A + X I X domains where A is a UFD, J. Pure Appl. Algebra, 160 (2001), 183-194. Zbl1001.13008MR1835999
  14. HALTER-KOCH, F., Factorization of algebraic integers, Ber. Math. Stat. Sektion im Forschungszentrum, 191 (1983), 1-24. Zbl0506.12005
  15. KIM, H., Examples of half-factorial domains, Canad. Math. Bull., 43 (2000), 362-367. Zbl1032.13010MR1776064
  16. PICAVET-L’HERMITTE, M., Factorization in some orders with a PID as integral closure, Algebraic number theory and Diophantine analysis (Graz, 1998), 365-390, de Gruyter, Berlin, 2000. Zbl0971.13016MR1770474
  17. ZAKS, A., Half factorial domains, Israel J. Math., 37 (1980), 281-302. Zbl0509.13017MR599463

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