On R-Ideals of a Dubrovin Valuation Ring R
On R-Ideals of a Dubrovin Valuation Ring R
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DOI：
10.1081/agb-120027865
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发表时间：
2004-03
影响因子：
0.7
通讯作者：
S. Irawati;H. Marubayashi;A. Ueda
中科院分区：
文献类型：
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作者：
S. Irawati;H. Marubayashi;A. Ueda
摘要如果R是Bezout， R/J(R)是简单Artinian环Q中的一个阶R是Dubrovin赋值环，其中J(R)是R的Jacobson根。本文研究了O R (I) = S = O l (I)的非有限生成的右R理想R-理想I。证明了S的某些稳定元素c和J(S)-初等理想a的I = cA。作为这一结果的应用，我们用稳定元素和初等理想描述了Q在其中心上是有限维的情况下的所有r -理想。
Abstract An order R in a simple Artinian ring Q is said to be a Dubrovin valuation ring if R is Bezout and R/J(R) is simple Artinian, where J(R) is the Jacobson radical of R. In this article, we shall investigate R-ideals I which are not finitely generated as a right R-ideal with O r (I) = S = O l (I). It is proved that I = cA for some stabilizing element c of S and for some J(S)-primary ideal A. As an application of this result, we describe all R-ideals in terms of stabilizing elements and primary ideals in the case Q is finite dimensional over its center.