Stability and Clifford regularity with respect to star operations

In the last few years, the concepts of stability and Clifford regularity have been fruitfully extended by using star operations. In this paper we deepen the study of star stable and star regular domains and relate these two classes of domains to each other.Comment: 22 pages; Comm. Alg., 201

Star Stable Domains

We introduce and study the notion of $\star$-stability with respect to a semistar operation $\star$ defined on a domain $R$; in particular we consider the case where $\star$ is the $w$-operation. This notion allows us to generalize and improve several properties of stable domains and totally divisorial domains.Comment: 21 pages. J. Pure Appl. Algebra, to appea

Star Stability and Star Regularity for Mori Domains

In the last few years, the concepts of stability and Clifford regularity have been fruitfully extended by using star operations. In this paper we study and put in relation these properties for Noetherian and Mori domains, substantially improving several results present in the literature.Comment: 14 pages; Rend. Semin. Mat. Univ. Padova, 201

Semistar Dedekind Domains

Let $D$ be an integral domain and $\star$ a semistar operation on $D$. As a generalization of the notion of Noetherian domains to the semistar setting, we say that $D$ is a $\star$--Noetherian domain if it has the ascending chain condition on the set of its quasi--$\star$--ideals. On the other hand, as an extension the notion of Pr\"ufer domain (and of Pr\"{u}fer $v$--multiplication domain), we say that $D$ is a Pr\"ufer $\star$--multiplication domain (P$\star$MD, for short) if $D_M$ is a valuation domain, for each quasi--$\star_{_{f}}$--maximal ideal $M$ of $D$. Finally, recalling that a Dedekind domain is a Noetherian Pr\"{u}fer domain, we define a $\star$--Dedekind domain to be an integral domain which is $\star$--Noetherian and a P$\star$MD. In the present paper, after a preliminary study of $\star$--Noetherian domains, we investigate the $\star$--Dedekind domains. We extend to the $\star$--Dedekind domains the main classical results and several characterizations proven for Dedekind domains. In particular, we obtain a characterization of a $\star$--Dedekind domain by a property of decomposition of any semistar ideal into a ``semistar product'' of prime ideals. Moreover, we show that an integral domain $D$ is a $\star$--Dedekind domain if and only if the Nagata semistar domain Na$(D, \star)$ is a Dedekind domain. Several applications of the general results are given for special cases of the semistar operation $\star$

Star-Invertibility and tt-finite character in Integral Domains

Let $A$ be an integral domain. We study new conditions on families of integral ideals of $A$ in order to get that $A$ is of $t$-finite character (i.e., each nonzero element of $A$ is contained in finitely many $t$-maximal ideals). We also investigate problems connected with the local invertibility of ideals.Comment: 16 page

I beni culturali di interesse religioso nella nuova legislazione statale: le innovazioni nell'Intesa con la Conferenza episcoipale italiana

La nuova Intesa tra il Ministro per i Beni e le Attivit\ue0 culturali ed il Presidente della Conferenza episcopale italiana si \ue8 resa necessaria a seguito dell\u2019entrata in vigore del d.lgs. 22 gennaio 2004, n. 42 (Codice dei beni culturali e del paesaggio) e della l. cost. 18 ottobre 2001, n. 3 (modifiche al Titolo V della Costituzione). Sul piano strutturale il documento, in diverse circostanze, ripropone i contenuti sostanziali dell\u2019Intesa del 1996 (che trascurer\uf2 in quanto diffusamente trattati dalla dottrina) ma in pi\uf9 punti \uabaggiorna\ubb e \uabintegra\ubb, per usare la stessa terminologia adottata in sede di sottoscrizione, i contenuti della precedente Intesa. Pertanto in questa sede cercher\uf2 di evidenziare e circoscrivere alcune criticit\ue0 di sistema, se tali saranno anche nelle applicazioni, in rapporto alle intervenute innovazioni legislative

Exotic Matter research in Space

The direct detection of annihilation products in cosmic rays offer an alternative way to search for dark matter particles candidates. Here we will see in particular that the study of the spectrum of antiproton and positrons offer good possibilities to perform this search and we will review our experimental effort in this direction.Comment: 10 pages, 2 figures, Invited talk at the Ninth Marcel Grossmann Meeting, Rome, July 2 - 8, 200