The reduction number of stretched ideals

Abstract: The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the structure of the associated graded ring of stretched $\mathfrak m $-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring $(A,\mathfrak m )$. As an application, we present complete descriptions of the associated graded ring of stretched $\mathfrak m $-primary ideals with small reduction number.

Mathematics

Audience: advanced learners

IIT Bombay Virtual Commutative Algebra Seminar

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