On domains with ACC on invertible ideals

Stefania Gabelli

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1988)

  • Volume: 82, Issue: 3, page 419-422
  • ISSN: 1120-6330

Abstract

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If A is a domain with the ascending chain condition on (integral) invertible ideals, then the group I ⁢ ( A ) of its invertible ideals is generated by the set I m ⁢ ( A ) of maximal invertible ideals. In this note we study some properties of I m ⁢ ( A ) and we prove that, if I ⁢ ( A ) is a free group on I m ⁢ ( A ) , then A is a locally factorial Krull domain.

How to cite

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Gabelli, Stefania. "On domains with ACC on invertible ideals." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 82.3 (1988): 419-422. <http://eudml.org/doc/287370>.

@article{Gabelli1988,
abstract = {If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_\{m\}(A)$ of maximal invertible ideals. In this note we study some properties of $I_\{m\}(A)$ and we prove that, if $I(A)$ is a free group on $I_\{m\}(A)$, then $A$ is a locally factorial Krull domain.},
author = {Gabelli, Stefania},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Krull domain; Locally factorial; Invertible ideal; integral domain; ascending chain condition; invertible ideals; divisorial ideal; locally factorial Krull domain},
language = {eng},
month = {9},
number = {3},
pages = {419-422},
publisher = {Accademia Nazionale dei Lincei},
title = {On domains with ACC on invertible ideals},
url = {http://eudml.org/doc/287370},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Gabelli, Stefania
TI - On domains with ACC on invertible ideals
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1988/9//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 3
SP - 419
EP - 422
AB - If $A$ is a domain with the ascending chain condition on (integral) invertible ideals, then the group $I(A)$ of its invertible ideals is generated by the set $I_{m}(A)$ of maximal invertible ideals. In this note we study some properties of $I_{m}(A)$ and we prove that, if $I(A)$ is a free group on $I_{m}(A)$, then $A$ is a locally factorial Krull domain.
LA - eng
KW - Krull domain; Locally factorial; Invertible ideal; integral domain; ascending chain condition; invertible ideals; divisorial ideal; locally factorial Krull domain
UR - http://eudml.org/doc/287370
ER -

References

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  2. ANDERSON, D.D. and ANDERSON, D.F., Generalized GCD domains, Comment. Math. Univ. St. Pauli, 28 (2) (1979), 215-221. Zbl0434.13001MR578675
  3. BARUCCI, V., DOBBS, D.E. and FONTANA, M., Conducive integral domains as pullbacks, Manuscripta Math.54, (1986), 261-267. Zbl0585.13013MR819402DOI10.1007/BF01171337
  4. BARUCCI, V. and GABELLI, S., How far is a Mori domain from being a Krull domain?, J. Pure Appl. Algebra, 45 (1987), 101-112. Zbl0623.13008MR889586DOI10.1016/0022-4049(87)90063-6
  5. BARUCCI, V. and GABELLI, S., On the class Group of a Mori domain, J. Algebra, 108 (1987), 161-173. Zbl0623.13009MR887199DOI10.1016/0021-8693(87)90129-3
  6. FOSSUM, R., The divisor Class Group of a Krull domain, Springer-Verlag, 1973. Zbl0256.13001MR382254
  7. GABELLI, S., Completely integrally closed domains and t-ideals, Boll. UMI, (7) 3-B (1989). Zbl0677.13007MR997999
  8. GILMER, R., Multiplicative ideal theory, Queen's Paper in Pure and Applied Mathematics, No 12, 1968. Zbl0804.13001MR229624
  9. GRECO, S., Sugli ideali frazionari invertibili, Rend. Sem. Mat. Padova, 36 (1966), 315-333. Zbl0144.02801MR201461

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