We explicitly calculate the normal cones of all monomial primes which define the curves of the form (tL, tL+1, . . . , tL+n), where n ≤ 4. All of these normal cones are reduced and Cohen-Macaulay, and their reduction numbers are independent of the reduction. These monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integr...

The basis of this study, which was put forth in order to appropriate a special area the hyperring theory, has recently been studied as generalization ring uses module theory an application field, is based on integrally closed Krasner hyperrings and (almost) integral dependence applications krasner hyperrings.

In this paper, we give a generalization of the integral dependence from rings to modules. We study the stability of the integral closure with respect to various module theoretic constructions. Moreover, we introduce the notion of integral extension of a module and prove the Lying over, Going up and Going down theorems for modules.

We study semigroup C*-algebras of ax + b-semigroups over integral domains. The goal is to generalize several results about C*-algebras of ax + bsemigroups over rings of algebraic integers. We prove results concerning K-theory and structural properties like the ideal structure or pure infiniteness. Our methods allow us to treat ax+b-semigroups over a large class of integral domains containing al...