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Paper   IPM / M / 16184
School of Mathematics
  Title:   Quintessential-Modulated Ideals
  Author(s):  Tirdad Sharif (Joint with S. Jahandoust)
  Status:   Published
  Journal: J. Algebra
  Vol.:  564
  Year:  2020
  Pages:   119-150
  Supported by:  IPM
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 Ratli [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- Ratli 's results [8, 13].

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