Abstract. Let R denote a commutative Noetherian ring and let I be an ideal of R such that H i I (R) = 0, for all integers i ≥ 2. In this paper we shall prove some results concerning the homological properties of I.

Let (R, m) be a Cohen–Macaulay local ring of dimension d, C a canonical R-module and M an almost Cohen–Macaulay R-module of dimension n and of depth t. We prove that dim [Formula: see text] and if [Formula: see text] then [Formula: see text] is an almost Cohen–Macaulay R-module. In particular, if [Formula: see text] then HomR(M, C) is an almost Cohen–Macaulay R-module. In addition, with some conditions, we show that [Formula: see text] is also almost Cohen–Macaulay. Finally, we study the vanishing [Formula: see text] and [Formula: see text].

Abstract. Let I and J be two ideals of a commutative Noetherian ring R and M be an R-module. For a non-negative integer n it is shown that, if the sets Ass R (Ext

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