Let  be a local Cohen-Macaulay ring with infinite residue field,  an Cohen - Macaulay module and  an ideal of  Consider  and , respectively, the Rees Algebra and associated graded ring of , and denote by  the analytic spread of  Burch’s inequality says that  and equality holds if  is Cohen-Macaulay. Thus, in that case one can compute the depth of associated graded ring of  as  In this paper we ...

The production of serotonin (5-hydroxtryptamine) and certain related metabolites by tumours associated with the clinical carcinoid syndrome has now been well established. Many of the reported cases have concerned carcinoid tumours of the intestinal tract (Thorson, 1958 ; Macfarlane, Dalgliesh, Dutton, Lennox, Nyhus, and Smith, 1956) but tumours histologically resembling carcinoids, and also app...

This text is a further elaboration of the previous research report [5]. Graded properties of binary and unary connectives valued in MTL4-algebras are studied in the framework of Fuzzy Class Theory (or higher-order fuzzy logic) FCT, which serves as a tool for easy derivation of graded theorems. The properties studied include graded monotonicity, a generalized Lipschitz property, commutativity, a...

Let Δ be an abelian group. By considering the notion multiplication of Δ-graded modules (see [7]) over a commutative Δ-graded ring with unity, we introduce the notion of product of two Δ-graded submodules which we use to characterize the Δ-graded prime submodules of a multiplication Δ-graded module. Finally we proved a graded version of Nakayama lemma for multiplication Δ-graded modules.

A semi-analytical method is used to study the effects of the multi vibration absorbers on the nonlinear functionally graded (FG) Euler-Bernoulli beam subjected to periodic load. The material properties of the beam are assumed to be continuously graded in the thickness direction. The governing equations of functionally graded beam are obtained based on the Hamilton's principle and these equation...