The concepts of ∗-relation of a (Γ-)semigroup and Γ̄-adequate transversal of a (Γ-)abundant semigroup are defined in this note. Then we develop a matrix type theory for abundant semigroups. We give some equivalent conditions of a Rees matrix semigroup being abundant and some equivalent conditions of an abundant Rees matrix semigroup having an adequate transversal. Then we obtain some Rees matrix...

We provide the sufficient conditions for Rees algebras of modules to be Cohen-Macaulay, which has been proven in the case of Rees algebras of ideals in [11] and [4]. As it turns out the generalization from ideals to modules is not just a routine generalization, but requires a great deal of technical development. We use the technique of generic Bourbaki ideals introduced by Simis, Ulrich and Vas...

The fluorescence emission maximum of a polar fluorophore in viscous medium often shows a dependence on excitation wavelength, a phenomenon which is named red edge excitation shift (REES). We have found that the fluorescence spectra of the tubulin tryptophans exhibit a REES of about 7 nm. Also, their steady state fluorescence polarization and mean lifetimes show a dependence on both excitation a...

The aim of this paper is to study integer rounding properties of various systems of linear inequalities to gain insight about the algebraic properties of Rees algebras of monomial ideals and monomial subrings. We study the normality and Gorenstein property—as well as the canonical module and the a-invariant—of Rees algebras and subrings arising from systems with the integer rounding property. W...

We compute the canonical class of certain Rees algebras. Our formula generalizes that of Herzog and Vasconcelos. Its proof relies on the fact that the formation of the canonical module commutes with subintersections in important cases. As an application we treat the classical determinantal ideals and the corresponding algebras of minors. A considerable part of Wolmer Vasconcelos’ work has been ...

We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allow the use of deformation theory. One can talk about the (essentially unique) Bourbaki ideal I(E) of a module E which, in many situations, allows to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Maca...

Let (R, m) be a local ring of Krull dimension d and I ⊆ R be an ideal with analytic spread d. We show that the j-multiplicity of I is determined by the Rees valuations of I centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at an O(nd) rate.

We prove that the elements of any standard basis of In, where I is an ideal of a Noetherian local ring and n is a positive integer, have order bounded by a linear function in n. We deduce from this that the elements of any standard basis of In in the sense of Grauert-Hironaka, where I is an ideal of the ring of power series, have order bounded by a polynomial function in n. The aim of this pape...

Previous studies on rare earth element (REE) bioaccumulation have focused on their accumulation rate and fractionation, but the processes involved remain unclear. In this study, the accumulation and fractionation of REEs in wheat (Triticum aestivum L.) were investigated using solution culture with exogenous mixed REEs. A decrease in REE contents was observed from the roots to the tops of wheat....