纯整环并半环的半群结构

环并半环称为纯整环并半环, 若其加法幂等元集是一个带半环. 若纯整环并半环的加法幂等元集是一个T带半环, 称为$T$纯整环并半环. 研究了纯整环并半环以及一些$T$纯整环并半环的半群结构.     

新型软半环

将软集的参数集赋予半环的代数结构,提出新型软半环的概念,并利用对偶软集的方法给出新型软半环的等价刻画;然后讨论了两个新型软半环在限制交和且等运算下仍然是新型软半环的性质;最后得到新型软半环的同态像和原像仍然是新型软半环的结论.     

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.     

满足a+ab=a+b的幂等半环的结构

本文讨论了满足a+ab=a+b的幂等半环的结构,给出这种幂等半环是左零半环的伪强右正规幂等半环,并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环.     

新型软半环北大核心

将软集的参数集赋予半环的代数结构,提出新型软半环的概念,并利用对偶软集的方法给出新型软半环的等价刻画;然后讨论了两个新型软半环在限制交和且等运算下仍然是新型软半环的性质;最后得到新型软半环的同态像和原像仍然是新型软半环的结论.     

链式条件下的半环的(∈,∈∨q(λ,μ))-模糊双理想

给出双诺特半环、双阿丁半环的概念。通过使用半环的双理想族建立半环的(∈,∈∨q(λ,μ))-模糊双理想。利用(∈,∈∨q(λ,μ))-模糊双理想刻画双诺特半环、双阿丁半环。     

Ω-模糊可补子半环

给定一个集合Ω,引入了可补半环的Ω-模糊可补子半环的概念,研究了它的一些基本性质。给出了可补半环的Ω-模糊可补子半环的等价刻画,证明了可补半环的Ω-模糊可补子半环的交、同态像与同态原像等也是可补半环的Ω-模糊可补子半环。最后,通过在SΩ上定义运算+,×,-,得到可补半环(SΩ,+,×,-),并研究了与其相关的模糊可补子半环与Ω-模糊可补子半环。     

一类平坦半环生成的簇

平坦半环是一类重要的加法幂等元半环,它在半环簇理论的研究中扮演着重要的角色.主要研究了次直不可约的平坦半环,以及一类平坦半环生成的簇.给出了次直不可约的nil-平坦半环的等价刻画,证明了当n小于4时,平坦半环S(x1x2…xn)均是有限基底的.     

满足a＋ab=a＋b幂等半环的结构

本讨论了满足a ab=a b的幂等半环的结构，给出了这种幂等半环是左零半环的伪强右正规幂等半环，并得出这种幂等半环与环的直积是左环的伪强右正规幂等半环。     

关于满足ACC的*-λ-半环

从满足ACC的任何偏序集是pre-CPO出发,研究了满足ACC的偏序集上的定向集,并由此给出满足ACC的＊-λ-半环的一些性质.证明了S是满足ACC的＊-λ-半环,则S是局部闭＊-半环和连续＊-半环.进一步得到任何满足ACC的＊-λ-半环是对称＊-λ-半环。     

on O-simple semirings,semigroup semirings,and two kinds of division semirings

In this paper we consider O-simple semirings S, where O denotes the multiplicative zero of S, which may be in particular the additive neutral o of S at the same time. In this context we give some statements on matrix semirings and introduce contracted semigroup semirings in §3, a matter of interest of its own. We further use our results to compare the usual concept of division semirings with a new one introduced in [18], and we show that a corresponding theorem in [18] is in general only valid for division semirings in the usual meaning. Dedicated to E.S. Lyapin on his 70th birthday     

几类加法非正则半环

In this paper, we introduce Green＇s .-relations on semirings and define [left, right] adequate semirings to explore additively non-regular semirings. We characterize the semirings which are strong b-lattices of [left, right] skew-halfrings. Also, as further generalization, the semirings are described which are subdirect products of an additively commutative idempotent semiring and a [left, right] skew-halfring. We extend results of constructions of generalized Clifford semirings （given by M. K. Sen, S. K. MaRy, K. P. Shum, 2005） and the semirings which are subdirect products of a distributive lattice and a ring （given by S. Ghosh, 1999） to additively non-regular semirings.     

FP-injective semirings,semigroup rings and Leavitt path algebras

In this paper we give characterisations of FP-injective semirings (previously termed “exact” semirings in work of the first author). We provide a basic connection between FP-injective semirings and P-injective semirings, and establish that FP-injectivity of semirings is a Morita invariant property. We show that the analogue of the Faith-Menal conjecture (relating FP-injectivity and self-injectivity for rings satisfying certain chain conditions) does not hold for semirings. We prove that the semigroup ring of a locally finite inverse monoid over an FP-injective ring is FP-injective and give a criterion for the Leavitt path algebra of a finite graph to be FP-injective.     

The semiring of continous [0, 1]-valued functions

In this paper, we study the properties of prime ideals in semirings of continuous functions with values in the unit interval [0, 1] on topological spaces. We describe maximal and pure ideals of such semirings. We study homomorphisms of semirings of continuous [0, 1]-valued functions. In terms of semirings of functions we characterize some properties of compacta. We show that the theory of ideals in these semirings differs from the case of rings of continuous functions.     

Distributive lattice decompositions of semirings with a semilattice additive reduct

We describe the least distributive lattice congruence on the semirings in the variety of all semirings whose additive reduct is a semilattice, introduce the notion of a k-Archimedean semiring and characterize the semirings that are distributive lattices or chains of k-Archimedean semirings.     

The Semigroup Structure of Left Clifford Semirings

In this paper,we generalize Clifford semirings to left Clifford semirings by means of the so-called band semirings.We also discuss a special case of this kind of semirings,that is, strong distributive lattices of left rings.     

Reduced Rickart semirings and their functional representations

In this paper, we consider reduced semirings with supplementary conditions of annihilators, namely these are Rickart and weakly Rickart semirings. The main aim of the paper is to study functional representations of semirings. We build two sheaves of semirings and prove that a reduced Rickart semiring is presented by sections of these sheaves. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 205–215, 2007.     

Pseudocomplementation and minimal prime ideals in semirings

In Section 2 of the present paper, we introduce the concept of pseudocomplementation for semirings and show the semiring version of some known results in lattice theory. We also introduce semirings with pc-functions and prove some interesting results for minimal prime ideals of such semirings. In Section 3, some classical results for minimal prime ideals in ring theory are generalized in the context of semiring theory.     

On V-semirings and Semirings All of Whose Cyclic Semimodules Are Injective

In this article, we introduce and study V- and CI-semirings—semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings and establish some fundamental properties of V-semirings. We show that all Jacobson-semisimple V-semirings are V-rings. We also completely describe the bounded distributive lattices, Gelfand, subtractive, semisimple, and antibounded, semirings that are CI-semirings. Applying these results, we give complete characterizations of congruence-simple subtractive and congruence-simple antibounded CI-semirings which solve two earlier open problems for these classes of CI-semirings.     

Linear operators that preserve maximal column rank of boolean matrices

This paper concerns two notions of column rank of matrices over semirings; column rank and maximal column rank. These two notions are the same over fields but differ for matrices over certain semirings. We determine how much the maximal column rank is different from the column ran for all m×n matrices over many semirings. We also characterize the linear operators which preserve the maximal column rank of Boolean matrices.