Okounkov Bodies of Finitely Generated Divisors

Chebyshev transforms on Okounkov bodies

LetL be a big holomorphic line bundle on a compact complex manifoldX.We show how to associate a convex function on the Okounkov body ofL to any continuous metric e−ψ on L.We will call this the Chebyshev transform of ψ, denoted by c[ψ]. Our main theorem states that the integral of the difference of the Chebyshev transforms of two weights is equal to the relative energy of the weights, which is a...

A characterization of finitely generated multiplication modules

 Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

Ring With All Finitely Generated Modules Retractable

Presentations of Finitely Generated Submonoids of Finitely Generated Commutative Monoids

We give an algorithmic method for computing a presentation of any finitely generated submonoid of a finitely generated commutative monoid. We use this method also for calculating the intersection of two congruences on Np and for deciding whether or not a given finitely generated commutative monoid is t-torsion free and/or separative. The last section is devoted to the resolution of some simple ...

MULTIPLICATION MODULES THAT ARE FINITELY GENERATED

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$. It is shown that over a Noetherian domain $R$ with dim$(R)leq 1$, multiplication modules are precisely cyclic or isomorphic to an invertible ideal of $R$. Moreover, we give a charac...