Star-invertible ideals of integral domains

Gyu Whan Chang; Jeanam Park

Bollettino dell'Unione Matematica Italiana (2003)

  • Volume: 6-B, Issue: 1, page 141-150
  • ISSN: 0392-4041

Abstract

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Let ∗ be a star-operation on R and ∗ s the finite character star-operation induced by ∗ . The purpose of this paper is to study when ∗ = v or ∗ s = t . In particular, we prove that if every prime ideal of R is ∗ -invertible, then ∗ = v , and that if R is a unique ∗ -factorable domain, then R is a Krull domain.

How to cite

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Chang, Gyu Whan, and Park, Jeanam. "Star-invertible ideals of integral domains." Bollettino dell'Unione Matematica Italiana 6-B.1 (2003): 141-150. <http://eudml.org/doc/195792>.

@article{Chang2003,
abstract = {Let $\ast$ be a star-operation on $R$ and $\ast_\{s\}$ the finite character star-operation induced by $\ast$. The purpose of this paper is to study when $\ast=v$ or $\ast_\{s\}=t$. In particular, we prove that if every prime ideal of $R$ is $\ast$-invertible, then $\ast=v$, and that if $R$ is a unique $\ast$-factorable domain, then $R$ is a Krull domain.},
author = {Chang, Gyu Whan, Park, Jeanam},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {141-150},
publisher = {Unione Matematica Italiana},
title = {Star-invertible ideals of integral domains},
url = {http://eudml.org/doc/195792},
volume = {6-B},
year = {2003},
}

TY - JOUR
AU - Chang, Gyu Whan
AU - Park, Jeanam
TI - Star-invertible ideals of integral domains
JO - Bollettino dell'Unione Matematica Italiana
DA - 2003/2//
PB - Unione Matematica Italiana
VL - 6-B
IS - 1
SP - 141
EP - 150
AB - Let $\ast$ be a star-operation on $R$ and $\ast_{s}$ the finite character star-operation induced by $\ast$. The purpose of this paper is to study when $\ast=v$ or $\ast_{s}=t$. In particular, we prove that if every prime ideal of $R$ is $\ast$-invertible, then $\ast=v$, and that if $R$ is a unique $\ast$-factorable domain, then $R$ is a Krull domain.
LA - eng
UR - http://eudml.org/doc/195792
ER -

References

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  1. ANDERSON, D. D.- ZAFRULLAH, M., On t -invertibility, IV, Factorization in Integral Domains, Lecture Notes in Pure and Applied Math., Marcel Dekker, 189 (1997), 221-225. Zbl0882.13001MR1460774
  2. ANDERSON, D. F., A general theory of class groups, Comm. Algebra, 16 (4) (1988), 805-847. Zbl0648.13002MR932636
  3. ANDERSON, D. F.- KIM, H.- PARK, J., Factorable domains, to appear in Comm. Algebra. Zbl1088.13512MR1936459
  4. GILMER, R., Multiplicative Ideal Theory, Marcel Dekker, New York, 1972. Zbl0248.13001MR427289
  5. HOUSTON, E.- ZAFRULLAH, M., On t -invertibility, II, Comm. Algebra, 17 (1989), 1955-1969. Zbl0717.13002MR1013476
  6. JAFFARD, P., Les systèmes d'Idéaux, Dunod, Paris, 1960. Zbl0101.27502MR114810
  7. KANG, B. G., On the converse of a well-known fact about Krull domains, J. Algebra, 124 (1989), 284-299. Zbl0694.13011MR1011595
  8. KANG, B. G., Prüfer v -multiplication domains and the ring R ⁢ X N v , J. Algebra, 123 (1989), 151-170. Zbl0668.13002MR1000481
  9. KAPLANSKY, I., Commutative Rings, revised edition, Univ. of Chicago Press, 1974. Zbl0296.13001MR345945

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