In this paper, by using elementary tools of commutative algebra,we prove the persistence property for two especial classes of rings. In fact, thispaper has two main sections. In the first main section, we let R be a Dedekindring and I be a proper ideal of R. We prove that if I1, . . . , In are non-zeroproper ideals of R, then Ass1(Ik11 . . . Iknn ) = Ass1(Ik11 ) [ · · · [ Ass1(Iknn )for all k1,...

Finding minimum-weight spanning trees (MST) in graphs is a classic problem in operations research with important applications in network design. The basic MST problem can be solved eeciently, but the degree constrained and multiobjective versions are NP-hard. Current approaches to the degree-constrained single objective MST include Raidl's evolutionary algorithm (EA) which employs a direct tree...

Let R be a commutative ring with identity. An ideal I in R is called a multiplication ideal if every ideal contained in I is a multiple of I. Ohm's properties for nitely generated ideals in Pr ufer domains are investigated by Gilmer. These properties are generalized by Naoum and studied for nitely generated multiplication ideals. The purpose of this work is to generalize the results of Gilmer a...

Stable and reliable numerical integration of second-order radial equations in the fields classical black holes can be performed by using Pr\"ufer transformation passing to use phase functions, which allows uniquely selecting solutions with physical asymptotics calculations.

We give a necessary and suÆcient condition so that a system is internally stabilizable and we prove that any system de ned by a transfer matrix with entries in the eld of fractions K = Q(A) of A is internally stabilizable if and only if A is a Pr ufer domain. Hence, if A is a Pr ufer domain which is not a B ezout domain, then there exist some internal stabilizable plants which have no doubly ...

In this paper, we introduce the concept of fuzzy star-operations on an integral domain and show that the set of all fuzzy star-operations on the integral domain forms a complete lattice. We also characterize Pr3 ufer domains, psuedo-Dedekind domains, (generalized-) greatest common divisor domains, and other integral domains in terms of the invertibility of certain fractionary fuzzy ideals. c © ...

This paper describes a new encoding scheme for the representation of spanning trees This new encoding scheme is based on the factor ization of the determinant of the in degree matrix of the original graph Each factor represents a spanning tree if the determi nant corresponding to that factor is equal to one Our new determinant encoding will be compared to the Pr ufer encoding and to the node an...

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...

Let $\star$ be a star operation on ring extension $R\subseteq S$. A S$ is called
 Pr\"ufer $star$-multiplication (P$\star$ME) if $(R_{[\m]}, \m _{[\m]})$ Manis pair in $S$ for
 every $\star$-maximal ideal $\m$ of $R$. We establish some results operations, and we study P$\star$ME
 pullback diagrams type $\square$. show that, for a
 maximal $R$, the $R_{[\m]} \subseteq is&#x0D...

This paper develops a model for the forward and spot exchange rate which allows for the presence of a Markov switching risk premium in the forward market and considers the issue of testing for the unbiased forward exchange rate (UFER) hypothesis. Using US/UK data, it is shown that the UFER hypothesis cannot be rejected provided that instrumental variables are used to account for within-regime c...