| Title:
|
A characterization of Krull rings with zero divisors (English) |
| Author:
|
Halter-Koch, Franz |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
29 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
119-122 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is proved that a Marot ring is a Krull ring if and only if its monoid of regular elements is a Krull monoid. (English) |
| Keyword:
|
Krull ring |
| Keyword:
|
Marot ring |
| Keyword:
|
divisor theory |
| Keyword:
|
essential valuation |
| Keyword:
|
discrete rank one valuation ring |
| MSC:
|
13F05 |
| idZBL:
|
Zbl 0818.13011 |
| idMR:
|
MR1242634 |
| . |
| Date available:
|
2008-06-06T21:24:13Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107472 |
| . |
| Reference:
|
[1] Borewicz, Z. I., Shafarevich, I. R.: Number Theory, 3rd ed. (Russian).Moskva 1985. |
| Reference:
|
[2] Geroldinger, A.: On the arithmetic of certain not integrally closed noetherian domains.Comm. Alg. 19 (1991), 685-698. MR 1100372 |
| Reference:
|
[3] Halter-Koch, F.: Ein Approximationssatz für Halbgruppen mit Divisorentheorie.Result. Math. 19 (1991), 74-82. Zbl 0742.20060, MR 1091957 |
| Reference:
|
[4] Huckaba, J. A.: Commutative rings with zero divisors.Marcel Dekker, 1988. Zbl 0637.13001, MR 0938741 |
| Reference:
|
[5] Kang, B. G.: A characterization of Krull rings with zero divisors.J. Pure Appl. Algebra 72 (1991), 33-38. Zbl 0752.13014, MR 1115565 |
| Reference:
|
[6] Portelli, D., Spangher, W.: Krull rings with zero divisors.Comm. Alg. 11 (1983), 1817-1851. MR 0703237 |
| Reference:
|
[7] Skula, L.: On $c$-semigroups.Acta Arith. 31 (1976), 247-256. Zbl 0303.13014, MR 0444817 |
| . |
