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 almost Cohen-Macaulayness 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.
Categories: math.AC