The Lyubeznik numbers are invariants of a local ring containing a field that capture ring-
theoretic properties, but also have numerous connections to geometry and topology. We …

Let $ R= k [x_1,..., x_n] $ be the polynomial ring in $ n $ independent variables, where $ k $
is a field. In this work we will study Bass numbers of local cohomology modules $ H^ r_I (R) …

In this work, we introduce a new set of invariants associated to the linear strands of a
minimal free resolution of a. We also prove that these invariants satisfy some properties …

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We provide a formula (see Theorem 1.5) for the Matlis dual of the injective hull of R/p where
p is a one dimensional prime ideal in a local complete Gorenstein domain (R, m). This is …

Let (R, m) denote an n-dimensional Gorenstein ring. For an ideal I⊂ R with gradeI= c we
define new numerical invariants τi, j (I) as the socle dimensions of Hmi (HIn− j (R)). In case of …

Let I be an ideal of a Complete Cohen-Macaulay local ring R of dimension n. We wil show
that the natural homomorphism Rto HomR (HcI (KR), HcI (KR)) is an isomorphism provided …

Let I denote an ideal in a commutative Noetherian ring R. Let M be an R-module. The I-adic
completion is defined by ̂ M^ I= _ α M/I^ α MM^ I= lim← α M/I α M. Then M is called I-adic …

In this paper, we examine the Lyubeznik tables of two linked ideals I and J of a complete
regular local ring S containing a field. More precisely, we prove that the Lyubeznik tables of …

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