Test ideals play a crucial role in the theory of tight closure developed by Melvin Hochster and Craig Huneke. Recently, Karen Smith showed that test ideals are closely related to certain multiplier ideals that arise in vanishing theorems in algebraic geometry. In this paper we develop a generalization of the notion of test ideals: for complete local rings R and S, where S is a module-6nite exte...

(1.2) PV~V where p is defined by p(s, t) = (t, s), (s, tET). We shall assume throughout that T is arcwise connected. Let 77 be an associative and anticommutative graded if-algebra with unit 1, where ii is a field. We assume throughout that 77'= 0 if i<0, and 77° = 7C-1. Let 77+ denote the submodule spanned by the elements of positive degree. 77 is a Hopf algebra over K if there is an algebra ho...

in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

Let k be a field of positive characteristic and K = k(V ) a function field of a variety V over k and let AK be the ring of adéles of K with respect to the places on K corresponding to the divisors on V . Given a Drinfeld module Φ : F[t] → EndK(Ga) over K and a positive integer g we regard both K and AgK as Φ(Fp[t])-modules under the diagonal action induced by Φ. For Γ ⊆ K a finitely generated Φ...

In this article, we formalize a free Z-module and its property. In particular, we formalize the vector space of rational field corresponding to a free Z-module and prove formally that submodules of a free Z-module are free. Z-module is necassary for lattice problems LLL (Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic systems with lattice [20]. Some theorems in this arti...

In this paper we characterize the radical of an arbitrary‎ ‎submodule $N$ of a finitely generated free module $F$ over a‎ ‎commutatitve ring $R$ with identity‎. ‎Also we study submodules of‎ ‎$F$ which satisfy the radical formula‎. ‎Finally we derive‎ ‎necessary and sufficient conditions for $R$ to be a‎ ‎Pr$ddot{mbox{u}}$fer domain‎, ‎in terms of the radical of a‎ ‎cyclic submodule in $Rbigopl...

In this paper, we consider the problem of extending existing submodule construction techniques that have been developed for finite state models into more expressive and compact behavioral models that handle data through parameterized interactions, state variables and simple guards. We provide a behavioral model based on extended Input-Output Automata and describe an algorithm that provides the ...

This paper describes the electro-thermal design of a medium voltage modular multilevel converter prototype, from the submodule power semiconductor thermal requirements to the overall system level integration. The high number of semiconductors and capacitors involved are stressed differently depending on the actual operating conditions, as discussed in the paper. The presented design considers a...