S. Irawati, H. Marubayashi, A. Ueda
An order R in a simple Artinian ring Q is said to be a Dubrovin valuation ring if A is Bezout and R/J(R) is simple Artinian, where J(R) is the Jacobson radical of R. In this article, we shall investigate A-ideals I which are not finitely generated as a right R-ideal with Or(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.
Department of Mathematics, State University of Malang, Malang, Indonesia; Department of Mathematics, Naruto University of Education, Naruto, Tokushima, Japan; Department of Mathematics, Shimane University, Matsue, Shimane, Japan; Department of Mathematics, State University of Malang, Malang (65145), East Java, Jalan Surabaya No. 6, Indonesia
