Uppers to zero and semistar operations in polynomial rings

Given a stable semistar operation of finite type $\star$ on an integral domain $D$, we show that it is possible to define in a canonical way a stable semistar operation of finite type $[\star]$ on the polynomial ring $D[X]$, such that $D$ is a $\star$-quasi-Pr\"ufer domain if and only if each upper to zero in $D[X]$ is a quasi-$[\star]$-maximal ideal. This result completes the investigation initiated by Houston-Malik-Mott \cite[Section 2]{hmm} in the star operation setting. Moreover, we show that $D$ is a Pr\"ufer $\star$-multiplication (resp., a $\star$-Noetherian; a $\star$-Dedekind) domain if and only if $D[X]$ is a Pr\"ufer $[\star]$-multiplication (resp., a $[\star]$-Noetherian; a $[\star]$-Dedekind) domain. As an application of the techniques introduced here, we obtain a new interpretation of the Gabriel-Popescu localizing systems of finite type on an integral domain $D$ (Problem 45 of \cite{cg}), in terms of multiplicatively closed sets of the polynomial ring $D[X]$

Polynomial extensions of semistar operations

We provide a complete solution to the problem of extending arbitrary semistar operations of an integral domain $D$ to semistar operations of the polynomial ring $D[X]$. As an application, we show that one can reobtain the main results of some previous papers concerning the problem in the special cases of stable semistar operations of finite type or semistar operations defined by families of overrings. Finally, we investigate the behavior of the polynomial extensions of the most important and classical operations such as $d_D$, $v_D$, $t_D$, $w_D$ and $b_D$ operations

On Dedekind domains whose class groups are direct sums of cyclic groups

For a given family $(G_i)_{i \in \N}$ of finitely generated abelian groups, we construct a Dedekind domain $D$ having the following properties. \begin{enumerate} \item \Pic(D) \cong \bigoplus_{i \in \N}G_i. \item For each $i \in \N$, there exists a submonoid $S_i \subseteq D^{\bullet}$ with \Pic (D_{S_i}) \cong G_i. \item Each class of \Pic (D) and of all \Pic (D_{S_i}) contains infinitely many prime ideals. \end{enumerate} Furthermore, we study orders as well as sets of lengths in the Dedekind domain $D$ and in all its localizations $D_{S_i}$.Comment: Journal of Pure and Applied Algebra, to appea

Dynamic Analysis of a Monostable Fluid Amplifier

Mechanical Engineerin

The mãori language nest program: voices of language and culture revitalization in Aotearoa, New Zealand

This article features interviews with five Mãori teachers who have been  directly involved with Mãori education for many years. They present their ideas and practices concerning  both Kohanga Reo, the successful language nest program which has been key for the revitalization and regeneration of the Mãori language, in New Zealand, and Kura Kaupapa, the Mãori primary and secondary education program.  Mãori language nest, language endangerment, language revitalization. R e s u m o : Este artigo apresenta entrevistas com cinco professores Mãori que têm estado diretamente envolvidos com a educação Mãori por muitos anos. Eles apresentam suas idéias e práticas sobre Kohanga Reo, o programa bem sucedido de ninho de língua, que tem sido fundamental para a revitalização e regeneração da língua Mãori, na Nova Zelândia e também sobre Kura Kaupapa, o programa Mãori de educação primária e secundária.Este artigo apresenta entrevistas com cinco professores Mãori que têm estado diretamente envolvidos com a educação Mãori por muitos anos. Eles apresentam suas idéias e práticas sobre Kohanga Reo, o programa bem sucedido de ninho de língua, que tem sido fundamental para a revitalização e regeneração da língua Mãori, na Nova Zelândia e também sobre Kura Kaupapa, o programa Mãori de educação primária e secundária.&nbsp