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arXiv · 1602.07035

Star-reductions of ideals and Prufer v-multiplication domains

E. Houston·S. Kabbaj·A. Miomouni
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Abstract

Let R be a commutative ring and I an ideal of R. A sub-ideal J of I is a reduction of I if JI^n = I^n+1 for some positive integer n. The ring R has the (finite) basic ideal property if (finitely generated) ideals of R do not have proper reductions. Hays characterized (one-dimensional) Prufer domains as domains with the finite basic ideal property (basic ideal property). We extend Hays' results to Prufer v-multiplication domains by replacing "basic" with "w-basic," where w is a particular star operation. We also investigate relations among star-basic properties for certain star operations.

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E. Houston, S. Kabbaj, A. Miomouni. 2016-02-23. Star-reductions of ideals and Prufer v-multiplication domains. https://arxiv.org/abs/1602.07035

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