On<i>R</i>-Ideals of a Dubrovin Valuation Ring<i>R</i>

DOI Web Site 被引用文献1件

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公開日
2004-03
DOI
  • 10.1081/agb-120027865
公開者
Informa UK Limited

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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.

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