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1.
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.  相似文献   

2.
LI YONG-HUA  HE YONG 《东北数学》2010,26(4):289-303
In this paper we establish a construction of a class of left E-adequate semigroups by using semilattices of cancellative monoids and fundamental left E-adequate semigroups. We first introduce concepts of type μ^+(μ^*,μ ) abundant semigroups and type μ^+left E-adequate semigroups. In fact, regular semigroups are type μ^+abundant semigroups and inverse semigroups are type μ^+left E-adequate semigroups. Next, we construct a special kind of algebras called E^+-product. It is proved that every E^+-product is a type μ^+left E-adequate semigroup, and every type μ^+left E-adequate semigroup is isomorphic to an E^+-product of a semilattice of cancellative monoids with a fundamental left E-adequate semigroup. Finally, as a corollary of the main result, it is deduced that every inverse semigroup is isomorphic to an E^+-product of a Clifford semigroup by a fundamental inverse semigroup.  相似文献   

3.
A Hilbert transform for Hlder continuous circulant (2 × 2) matrix functions, on the d-summable (or fractal) boundary Γ of a Jordan domain Ω in R2n , has recently been introduced within the framework of Hermitean Clifford analysis. The main goal of the present paper is to estimate the Hlder norm of this Hermitean Hilbert transform. The expression for the upper bound of this norm is given in terms of the Hlder exponents, the diameter of Γ and a specific d-sum (d d) of the Whitney decomposition of Ω. The result is shown to include the case of a more standard Hilbert transform for domains with left Ahlfors-David regular boundary.  相似文献   

4.
HE Fu-li 《数学季刊》2014,(3):317-324
In this paper we consider several fundamental operators in complex Clifford algebra and show the close relationship of these operators. We also discuss a representation of the Lie algebra s[(z; C) and get several decompositions for Clifford algebra of even dimension under the action of these fundamental operators.  相似文献   

5.
We study another structure of so-called left C-wrpp semigroups. In particular, the concept of left △-product is extended and enriched. The aim of this paper is to give a construction of left C-wrpp semigroups by a left regular band and a strong semilattice of left-R cancellative monoids. Properties of left C-wrpp semigroups endowed with left △-products are particularly investigated.  相似文献   

6.
By the Plemelj formula and the compressed fixed point theorem,this paper discusses a kind of boundary value problem for hypermonogenic function vectors in Clifford analysis.And the paper proves the existence and uniqueness of the solution to the boundary value problem for hypermonogenic function vectors in Clifford analysis.  相似文献   

7.
陈培慈 《数学季刊》1994,9(3):95-101
In this paper,we define the left rank of a ring R and discuss the relatlons between a left ore reng R and its left classical quotient ring Q on the properties of their ideals and left ranks.Also we gave four equivalent types of the proposition:a ring R has a left classical quotient ring Q and Q is a division ring.As an application of this result,we gave a brief proof method which different from [2] on the theorem of the Goldie Prime rings.  相似文献   

8.
The Mehler Formula for the Generalized Clifford-Hermite Polynomials   总被引:1,自引:0,他引:1  
The Mehler formula for the Hermite polynomials allows for an integral representation of the one-dimensional Fractional Fourier transform. In this paper, we introduce a multi-dimensional Fractional Fourier transform in the framework of Clifford analysis. By showing that it coincides with the classical tensorial approach we are able to prove Mehler's formula for the generalized Clifford-Hermite polynomials of Clifford analysis.  相似文献   

9.
Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.  相似文献   

10.
In this paper, we introduce the fractional wavelet transformations(FrWT) involving Hankel–Clifford integral transformation(HClIT) on the positive half line and studied some of its basic properties. Also we obtain Parseval's relation and an inversion formula. Examples of fractional powers of Hankel–Clifford integral transformation(FrHClIT) and FrWT are given. Then, we introduce the concept of fractional wavelet packet transformations FrBWPT and FrWPIT, and investigate their properties.  相似文献   

11.
12.
《代数通讯》2013,41(7):2609-2615
Abstract

Regular semigroups S with the property eS ? Se or Se ? eS for all idempotents e ∈ S include all left and right Clifford semigroups. Characterizations of such semigroups are given and their structure investigated, in particular in terms of spined products of left and right Clifford semigroups with respect to Clifford semigroups.  相似文献   

13.
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.  相似文献   

14.
15.
16.
满足a+ab=a+b的幂等半环的结构   总被引:1,自引:0,他引:1  
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.  相似文献   

17.
Fuzzy semirings     
In this paper we initiate the study of fuzzy semirings and fuzzy A-semimodules where A is a semiring and A-semimodules are representations of A. In particular, semirings all of whose ideals are idempotent, called fully idempotent semirings, are investigated in a fuzzy context. It is proved, among other results, that a semiring A is fully idempotent if and only if the lattice of fuzzy ideals of A is distributive under the sum and product of fuzzy ideals. It is also shown that the set of proper fuzzy prime ideals of a fully idempotent semiring A admits the structure of a topological space, called the fuzzy prime spectrum of A.  相似文献   

18.
加法半群为正规纯整群的半环类记为ONBG,本文主要研究了ONBG中半环的一些性质和次直积分解.  相似文献   

19.
The structure of left C-rpp semigroups   总被引:21,自引:0,他引:21  
This paper studies the class of left Clifford-rpp semigroups and investigates the structure of their semi-spined products and semilattice decompositions. These semigroups are generalizations of left Clifford semigroups and Clifford-rpp semigroups. We also discuss some special cases such as when a semilattice decomposition becomes a strong semilattice decomposition and a semi-spined product becomes a spined product. Communicated by Boris Schein This research is jointly supported by a grant of National Natural Science Foundation of China and a small project grant #200.600.380 of CUHK.  相似文献   

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