论文信息 - Some Characterizations of Krull Monoids

Some Characterizations of Krull Monoids

In this paper, Kaplansky-type theorems are given to characterize GCD-monoids and valuation monoids. Also, (unique) r-factorable monoids are defined and it is shown that S is a Krull monoid if and only if S is a unique t-factorable (resp., w-factorable) monoid if and only if S is a t-factorable (resp., w-factorable) t-Prufer monoid.

Hwankoo Kim | Y. Park | M. Kim

[1] G. Chang,et al. Star-invertible ideals of integral domains , 2003 .

[2] D. Kwak,et al. Star-operations on semigroups , 2001 .

[3] Young Soo Park,et al. Krull Domains of Generalized Power Series , 2001 .

[4] U. Krause,et al. Monoids determined by a homogenous linear diophantine equation and the half-factorial property , 2000 .

[5] Hwankoo Kim. Kaplansky-type Theorems , 2000 .

[6] Ryuki Matsuda,et al. Note On Kaplansky's Commutative Rings , 1999 .

[7] R. McCasland,et al. On Strong Mori domains , 1999 .

[8] Franz Halter-Koch,et al. Ideal Systems: An Introduction to Multiplicative Ideal Theory , 1998 .

[9] R. Gilmer,et al. Commutative Semigroup Rings , 1984 .

[10] M. Dorofeeva,et al. Prüfer and Dedekind monoids II , 1974 .

[11] M. Ikeda. On a theorem of Kaplansky , 1952 .