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Quintessential-modulated ideals
Journal of Algebra ( IF 0.9 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.jalgebra.2020.07.024
Saeed Jahandoust , Tirdad Sharif

Abstract Let R denote a commutative Noetherian ring and I an ideal of R. The concept of quintessential sequences over zero ideal was introduced by McAdam and Ratliff (1985) [8] . They showed that these sequences enjoy many of the basic properties of asymptotic sequences over zero ideal. It was shown, that quintessential sequences over ideals I ≠ ( 0 ) R are not a good analogue of asymptotic sequences over I ≠ ( 0 ) R . By making use of the new concept of quintessential grade of an ideal over another ideal, we show that there exists a class of ideals I for which quintessential sequences over I are an excellent analogue of asymptotic sequences over I. Also, we give more results on quintessential sequences over an ideal and derive generalizations of some McAdam-Ratliff's results (1985) [8] , [13] .

中文翻译:

典型调制理想

摘要 让 R 表示一个可交换的 Noetherian 环,I 表示 R 的理想。McAdam 和 Ratliff (1985) [8] 引入了零理想上的典型序列的概念。他们表明,这些序列具有超过零理想的渐近序列的许多基本性质。结果表明,理想 I ≠ ( 0 ) R 上的典型序列不是 I ≠ ( 0 ) R 上渐近序列的好类比。通过利用一个理想对另一个理想的典型等级的新概念,我们证明存在一类理想 I,其中 I 上的典型序列是 I 上渐近序列的极好类比。此外,我们给出了更多关于一个理想的典型序列,并推导出某些 McAdam-Ratliff 的结果 (1985) [8]、[13] 的概括。
更新日期:2020-12-01
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