A characterization of Krull rings with zero divisors

Franz Halter-Koch

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 1-2, page 119-122
  • ISSN: 0044-8753

Abstract

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It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid.

How to cite

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Halter-Koch, Franz. "A characterization of Krull rings with zero divisors." Archivum Mathematicum 029.1-2 (1993): 119-122. <http://eudml.org/doc/247436>.

@article{Halter1993,
abstract = {It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid.},
author = {Halter-Koch, Franz},
journal = {Archivum Mathematicum},
keywords = {Krull ring; Marot ring; divisor theory; essential valuation; discrete rank one valuation ring; Marot ring; Krull ring},
language = {eng},
number = {1-2},
pages = {119-122},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {A characterization of Krull rings with zero divisors},
url = {http://eudml.org/doc/247436},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Halter-Koch, Franz
TI - A characterization of Krull rings with zero divisors
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 1-2
SP - 119
EP - 122
AB - It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid.
LA - eng
KW - Krull ring; Marot ring; divisor theory; essential valuation; discrete rank one valuation ring; Marot ring; Krull ring
UR - http://eudml.org/doc/247436
ER -

References

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  1. Number Theory, 3rd ed. (Russian), Moskva 1985. 
  2. On the arithmetic of certain not integrally closed noetherian domains, Comm. Alg. 19 (1991), 685-698. (1991) MR1100372
  3. Ein Approximationssatz für Halbgruppen mit Divisorentheorie, Result. Math. 19 (1991), 74-82. (1991) Zbl0742.20060MR1091957
  4. Commutative rings with zero divisors, Marcel Dekker, 1988. Zbl0637.13001MR0938741
  5. A characterization of Krull rings with zero divisors, J. Pure Appl. Algebra 72 (1991), 33-38. (1991) Zbl0752.13014MR1115565
  6. Krull rings with zero divisors, Comm. Alg. 11 (1983), 1817-1851. (1983) MR0703237
  7. On c -semigroups, Acta Arith. 31 (1976), 247-256. (1976) Zbl0303.13014MR0444817

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