当前位置: X-MOL 学术Commun. Algebra › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Results on the behavior of the Ratliff–Rush operation and the depth of the associated graded ring
Communications in Algebra ( IF 0.6 ) Pub Date : 2021-03-27 , DOI: 10.1080/00927872.2021.1897989
Ibrahim Al-Ayyoub 1, 2
Affiliation  

Abstract

We give a full characterization of the unique Ratliff–Rush complete ideals in the polynomial rings R with two variables over a field. For a class of monomial ideals in R, we investigate the Ratliff–Rush behavior of powers of these ideals and also the depth of their associated graded ring. Namely, we give some sufficient and some necessary conditions for this depth to be positive. The results of this paper allow us to answer several questions of [13 Heinzer, W., Johnston, B., Lantz, D., Shah, K. (1993). Coefficient ideals in and blowups of a commutative Noetherian domain. J. Algebra 162(2):355391. DOI: 10.1006/jabr.1993.1261.[Crossref], [Web of Science ®] , [Google Scholar]].



中文翻译:

Ratliff-Rush 操作的行为和相关分级环的深度的结果

摘要

我们给出了多项式环R 中唯一的 Ratliff-Rush 完全理想的完整特征,在一个域上具有两个变量。对于R 中的一类单项式理想,我们研究了这些理想的幂的 Ratliff-Rush 行为以及它们相关分级环的深度。也就是说,我们给出了这个深度为正的一些充分条件和一些必要条件。本文的结果使我们能够回答[ 13 Heinzer, W.Johnston, B.Lantz, D.Shah, K. ( 1993 )。可交换 Noetherian 域中的系数理想和爆炸J. 代数162(2): 355391。DOI:10.1006/jabr.1993.1261[Crossref]、[Web of Science®]、[  Google Scholar] ]。

更新日期:2021-03-27
down
wechat
bug