Prime Submodules And A Sheaf On The Prime Spectra Of Modules

We define and investigate a sheaf of modules on the prime spectra of modules and it is shown that there is an isomorphism between the sections of this sheaf and the ideal transform module

Linkage of modules over Cohen-Macaulay rings

Inspired by the works in linkage theory of ideals, the concept of sliding depth of extension modules is defined to prove the Cohen-Macaulyness of linked module if the base ring is merely Cohen-Macaulay. Some relations between this new condition and other module-theory conditions such as G-dimension and sequentially Cohen-Macaulay are established. By the way several already known theorems in linkage theory are improved or recovered by new approaches.Comment: 12 Page

Plane Cremona maps: saturation and regularity of the base ideal

One studies plane Cremona maps by focusing on the ideal theoretic and homological properties of its homogeneous base ideal ("indeterminacy locus"). The {\em leitmotiv} driving a good deal of the work is the relation between the base ideal and its saturation. As a preliminary one deals with the homological features of arbitrary codimension 2 homogeneous ideals in a polynomial ring in three variables over a field which are generated by three forms of the same degree. The results become sharp when the saturation is not generated in low degrees, a condition to be given a precise meaning. An implicit goal, illustrated in low degrees, is a homological classification of plane Cremona maps according to the respective homaloidal types. An additional piece of this work relates the base ideal of a rational map to a few additional homogeneous "companion" ideals, such as the integral closure, the $\boldsymbol\mu$-fat ideal and a seemingly novel ideal defined in terms of valuations.Comment: New version only 36 pages, one typo correcte

Open loci of ideals with applications to Birational maps

In this work we show that the loci of ideals in principal class, ideals of grade at least two, and ideals of maximal analytic spread are Zariski open sets in the parameter space. As an application, we show that the set of birational maps of {\it clear polynomial degree} $d$ over an arbitrary projective variety $X$, denoted by \Bir(X)_{d}, is a constructible set. This extends a previous result by Blanc and Furter.Comment: 19 pg

A note on quasi-Gorenstein rings

In this paper, after giving a criterion for a Noetherian local ring to be quasi-Gorenstein, we obtain some sufficient conditions for a quasi- Gorenstein ring to be Gorenstein. In the course, we provide a slight generalization of a theorem of Evans and Griffith.Comment: To appear in Arch. Mat

Metal concentrations in razor clam Solen dactylus (Von Cosel, 1989) (Bivalvia: Solenidae), sediments and water in Golshahr coast of Bandar Abbas, Persian Gulf

In a complementary field study, the concentrations of some metals (Cu, Ag, Pb, Zn, Ni, Co, Mn, Fe, As, Cd, Cr, Mg and Ba) were measured in clam Solen dactylus, sediments and water collected at two stations (Park-e-Qadir, 56° 20/ E, 27° 11/ and Nakhl-e-Nakhoda, 56° 23/ E, 27° 10/ N) of Bandar Abbas coastal waters of the Persian Gulf in November 2008 and February 2009 showing different contamination levels. Although there is little information on metal concentrations in macro-benthic animals in this area, this study, for the first time, reports the accumulation of some metals in S. dactylus in order to introduce this species as a bioindicator for this area. Results indicated that Mg and Fe were the two most abundant metals in clams and sediments. The maximum and minimum metal concentrations in clams belonged to Mg (3850-5040 µgg-1 dry wt) and Ag (0.30-0.40-0.58 µgg-1 dry wt), respectively. There was a significant relationship between the accumulation of metals in clams, sediment and water samples. A significant relationship between clam lengths and concentrations of Cu (positive) and Mg (negative) were observed. Our study also showed that variable metal concentrations were related to different sampling stations, seasons and their interactions as well. Bioaccumulation of metals in clams was significantly different for eight metal elements between start of the gametogenesis and ripeness stages. Our investigation indicated that the clam S. dactylus could be a useful bioindicator for Zinc