Inspired by recent work in the theory of central projections onto hyper-surfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert– Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symme...

in this article, we study the artin-rees property in  c(x), in the  rings of fractions of  c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if  z(f)  is an open p-space. a necessary and sufficient condition for the local rings of  c(x)   to be artin-rees rings is that each prime ideal in  c(x)  becomes minimal and it turns out that every local ring ...

Inspired by recent work in the theory of central projections onto hypersurfaces, we characterize self-linked perfect ideals of grade 2 as those with a Hilbert–Burch matrix that has a maximal symmetric subblock. We also prove that every Gorenstein perfect algebra of grade 1 can be presented, as a module, by a symmetric matrix. Both results are derived from the same elementary lemma about symmetr...

Different alloying concepts to trace deoxidation products, mainly aluminium oxides, using rare earth elements (REEs), were tested on the laboratory scale by melting trials with a high-frequency remelting furnace. Lanthanum and Cerium, which belong group of light REEs, used for these experiments. The formed multiphase inclusions characterized scanning electron microscopy energy dispersive spectr...

Rare earth elements (REEs) have been increasingly emitted into the 8 atmosphere with a worldwide increase in use of these metals. However, the research 9 on REEs in atmospheric particulates is fairly limited. In this paper, atmospheric 10 particulates including total suspended particulate (TSP) matter and particles with an 11 equivalent aerodynamic diameter less than 10 μm (PM10) were collected...

It has long been observed that rare earth elements (REEs) regulate multiple facets of plant growth and development. However, the underlying mechanisms remain largely unclear. Here, using electron microscopic autoradiography, we show the life cycle of a light REE (lanthanum) and a heavy REE (terbium) in horseradish leaf cells. Our data indicate that REEs were first anchored on the plasma membran...

Given two determinantal rings over a field k, we consider the Rees algebra of the diagonal ideal, the kernel of the multiplication map. The special fiber ring of the diagonal ideal is the homogeneous coordinate ring of the secant variety. When the Rees algebra and the symmetric algebra coincide, we show that the Rees algebra is CohenMacaulay.

The ability of organic matter as well as carbonate ions to extract rare earth elements (REEs) from sandy sediments of a Coastal Plain aquifer was investigated for unpurified organic matter from different sources (i.e., Mississippi River natural organic matter, Aldrich humic acid, Nordic aquatic fulvic acid, Suwannee River fulvic acid, and Suwannee River natural organic matter) and for extractio...