Let I = (x1 , . . . , xq ) be a square-free monomial ideal of a polynomial ring K[x1, . . . , xn] over an arbitrary field K and let A be the incidence matrix with column vectors v1, . . . , vq. We will establish some connections between algebraic properties of certain graded algebras associated to I and combinatorial optimization properties of certain polyhedrons and clutters associated to A an...

The concept of residual intersection, introduced by Artin and Nagata [l] in 1972, is a fruitful generalization of linkage as the following two examples attest. Let I be a strongly Cohen-Macaulay ideal in a CohenMacaulay local ring R. If Z satisfies the condition (G,), then Huneke [6, Proposition 4.31 has proved that the extended Rees algebra R[It, t‘1 is defined by an ideal which is obtained fr...

The determination of trace rare-earth elements (REEs) can be used for the assessment of environmental pollution, and is of great significance to the study of toxicity and toxicology in animals and plants. N, N, N', N'-tetraoctyl diglycolamide (TODGA) is an environmental friendly extractant that is highly selective to REEs. In this study, an analytical method was developed for the simultaneous d...

This expository paper contains history, definitions, constructions, and the basic properties of Rees valuations of ideals. A section is devoted to one-fibered ideals, that is, ideals with only one Rees valuation. Cutkosky [5] proved that there exists a two-dimensional complete Noetherian local integrally closed domain in which no zero-dimensional ideal is one-fibered. However, no concrete ring ...

We show that, for every pseudovariety of groups H, the pseudovariety H̄, consisting of all finite semigroups all of whose subgroups lie in H, is irreducible for join and the Mal’cev and semidirect products. The proof involves a Rees matrix construction which motivates the study of iterated Mal’cev products with the pseudovariety of bands. We further provide a strict infinite filtration for H̄ usi...

In order to investigate the behavior of rare earth elements (REEs) and uranium (U) in marine organism, the concentrations of REEs and U in some brown algae samples taken on the coast of Niigata Prefecture were determined. In addition, laboratory model experiment to uptake these elements using living and dried algae (Undaria pinnatifida and Sargassum hemiphyllum) was also carried out to survey t...

Let A be an algebra over a field K, m and n natural numbers P = (pji) fixed x matrix A. The K-vector space of all matrices the can made into with respect to following operation (o): B o C BPC. This is called Munn sandwich P. algebras such type arose as generalizations semigroup Rees semigroups which in turn are closely related simple semigroups. article describes generators defining relations M...

It was shown by van Rees [18] that a latin square of order n cannot have more than n(n− 1)/18 latin subsquares of order 3. He conjectured that this bound is only achieved if n is a power of 3. We show that it can only be achieved if n ≡ 3 mod 6. We also state several conditions that are equivalent to achieving the van Rees bound. One of these is that the Cayley table of a loop achieves the van ...

Rare earth elements (REEs) enriched fertilizers have been commonly used in China since the 1980s, thus inducing a growing concern about their environmental impact in agriculture. In this work, the effect of some light REEs nitrate mixture and La(3+) nitrate on seed germination, seedling growth and antioxidant metabolism in Triticum durum was investigated with the aim of clarifying the potential...