About the Notion of Semiring of Sets

We introduce a generalized notion of semiring and prove that all known properties that semirings have according to the old definition are preserved.     

Characteristics of Subtractive Anodic Stripping Voltammetry of Lead,Cadmium and Thallium at Silver‐Gold Alloy Electrodes

Silver‐gold alloy electrodes have been studied for the purpose of the quantitative determination of heavy metals by subtractive anodic stripping voltammetry, (SASV). The results have been compared with those obtained with the silver and gold electrodes. The 50/50 a/o Ag/Au alloy electrode is the most suitable for quantifying thallium in the presence of lead and cadmium. The separation of its peak from those of lead and cadmium is 200 mV, which is about twice the separation obtained on the pure metal electrodes and is also better than on mercury. The silver electrode is suitable for the simultaneous determination of thallium, lead and cadmium. The peaks of lead and cadmium overlap on the 50/50 alloy. Pure silver or pure gold can be used for simultaneous quantification of these two metals. The use of gold for quantifying lead and cadmium is more limited because the peak potential of cadmium is shifted in the negative direction as its concentration increases and at [Cd²⁺]>200 nM, the two peaks merge. SASV enables correction for background currents and is of utmost importance for obtaining well‐defined peaks. The peaks of lead, cadmium and thallium appear over a relatively narrow potential range (ca. 200 mV) on all the electrodes presented in this work. For this reason, the quantifying of a peak is based on the derivative at the inflection point of only one of its branches (ascending or descending). All SASV measurements were carried out without removal of oxygen.     

Characteristics of subtractive anodic stripping voltammetry of Pb and Cd at silver and gold electrodes

Silver and gold electrodes are useful for the quantitative determination of lead and cadmium with subtractive anodic stripping voltammetry (SASV). The use of SASV is essential for achieving good separation between the two peaks, to eliminate the interference of nitrates when cadmium is present and to allow analysis at very low concentrations without the removal of oxygen. The deposition and dissolution of Pb²⁺ and Cd²⁺ proceed at underpotential (UPD) on both electrodes. The UPD properties of the deposits are the main factor determining the analytical characteristics of the ASV method and are strongly affected by the type and concentration of the electrolyte. The effects of anions (Cl⁻, Br⁻, SO₄²⁻, NO₃⁻) and acids (HNO₃, HClO₄, H₂SO₄, HCl) are shown. The two electrodes complement each other and, in addition, enable the qualitative identification of Pb²⁺ and Cd²⁺, since the peaks appear in opposite order on the two electrodes. Analysis of mixtures of the two analytes is restricted on gold but not on silver. At gold the two peaks overlap: (i) at concentrations of cadmium higher than 250 nM at deposition times greater than 30 s, (ii) in the presence of copper at concentrations higher than 1 μM, and (iii) in the presence of Triton X-100 at concentrations above 10 mg/l. The repeatability at 10 nM analyte is better than 2.5%. The detection limits for Pb²⁺ and Cd²⁺ at 120 s deposition time and 3500 rpm rotation rate are: dl_Pb/Ag=0.04 nM; dl_Cd/Ag=0.7 nM; dl_Pb/Au=0.1 nM; dl_Cd/Au=0.3 nM. The analysis of lead and cadmium in natural waters has been performed.     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

Semiring unions of a ring and a half-body

We describe the structure of semirings which are unions of a ring and a half-body.     

分配格和素域生成的半环簇

Let V be the variety generated by two-element distributive lattice B2 and k prime fields Fp1,...,Fpk. That is to say that V = HSP{B2, Fp1,...,Fpk}. It is proved that the variety V is finitely based. Also, the two-element distributive lattice B2 and prime fields Fp1,..., Fpk are, up to isomorphism, the only subdirectly irreducible semirings in V. Some known results are extended and enriched.     

一类幂等半环的性质和结构

研究了加法半群为半格的半环类S+l中的乘法带半环和矩形带半环类BR中的乘法带半环;给出了ID半环中乘法带半环的结构定理,即ID∩.■°D=.■z∨.■z∨D.     

交换分配半环上的最小分配格同余

§ 1 .　Introduction　　AsemiringSisanalgebraicstructure(S ,+,·)consistingofanon emptysetStogetherwithtwobinaryoperations +and·onSsuchthat(S ,+)and(S ,·)aresemigroupsconnectedbyring likedistributivity[1 ] .AsemiringSiscalledacommutativesemiringif (S ,+)and(S ,·)arebothcommutative.AcommutativesemiringiscalledacommutativedistributivityifinStheadditionisdistributiveaboutmultiplication ,i.e.,ab +c =(a+c) (b+c) ,a +bc=(a +b) (a+c) holdsforalla ,b,c∈S[2 ] .Anequivalentrelationρonasemiring…     

(C)-半环范畴

建立了C—半环范畴的概念，讨论了C—半环范畴的一些基本性质，并且给出自由C—半环的一种构造方法，进而，给出了任意一族C—半环的积与上积的存在唯一性定理。