共查询到20条相似文献,搜索用时 109 毫秒
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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. 相似文献
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《纯粹数学与应用数学》2020,(2)
研究了由x2≈x确定的加法幂等元半环簇和xy≈zt确定的加法幂等元半环簇的并W (即包含上述两个簇的并集的最小的簇)的有限基底问题.证明了W是有限基底的,且W的子簇格是阶为312的分配格. 相似文献
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研究了加法半群是带,乘法半群是完全正则半群的半环上的格林关系,给出了˙L∧+D(+L,+R)是同余关系的充分必要条件,证明了由这些同余关系所决定的半环类都是半环簇,并给出了这些半环簇的Mal′cev积分解. 相似文献
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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. 相似文献
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半环R被称为实半环,若对于任意的n∈N,方程x1^2+…+xn^2=0在R中只有零解:x1=…=xn=0.为了刻画实半环,引入了实理想和极小素理想的概念,利用同余的方法,得到了可减半环类中实半环的结构定理. 相似文献
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D. V. Skokov 《Russian Mathematics (Iz VUZ)》2018,62(9):52-59
We completely describe all commutative epigroup varieties that are cancellable elements of the lattice EPI of all epigroup varieties. In particular, we prove that a commutative epigroup variety is a cancellable element of the lattice EPI if and only if it is a modular element of this lattice. 相似文献
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Varieties of idempotent semirings with commutative addition 总被引:3,自引:0,他引:3
The multiplicative reduct of an idempotent semiring with commutative addition is a regular band. Accordingly there are 13
distinct varieties consisting of idempotent semirings with commutative addition corresponding to the 13 subvarieties of the
variety of regular bands. The lattice generated by the these 13 semiring varieties is described and models for the semirings
free in these varieties are given.
Received April 22, 2004; accepted in final form June 3, 2005. 相似文献
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Zur Izhakian 《代数通讯》2013,41(4):1445-1468
This article introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e., summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a tropical matrix is invertible if and only if it is regular. 相似文献
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Xianzhong Zhao 《Monatshefte für Mathematik》2005,75(1):157-167
Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring. 相似文献
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Xianzhong Zhao 《Monatshefte für Mathematik》2005,144(2):157-167
Locally closed semirings, iteration semirings and Conway semirings play an important role in the algebraic theory of semirings and theoretical computer science. Z. ésik and W. Kuich showed that a locally closed commutative semiring is an iteration semiring (is also a Conway semiring). By study of polynomial semirings and matrix semirings, we obtain new expressions of certain polynomials and show that all matrix semirings over a locally closed semiring are also locally closed, and so a locally closed semiring (which need not be commutative) is an iteration semiring. 相似文献
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We calculate the diameters of commuting graphs of matrices over the binary Boolean semiring, the tropical semiring and an
arbitrary nonentire commutative semiring. We also find the lower bound for the diameter of the commuting graph of the semigroup
of matrices over an arbitrary commutative entire antinegative semiring. 相似文献
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Yi-Jia Tan 《Linear and Multilinear Algebra》2013,61(4):498-517
In this paper, the concept of determinants for the matrices over a commutative semiring is introduced, and a development of determinantal identities is presented. This includes a generalization of the Laplace and Binet–Cauchy Theorems, as well as on adjoint matrices. Also, the determinants and the adjoint matrices over a commutative difference-ordered semiring are discussed and some inequalities for the determinants and for the adjoint matrices are obtained. The main results in this paper generalize the corresponding results for matrices over commutative rings, for fuzzy matrices, for lattice matrices and for incline matrices. 相似文献
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Yi-Jia Tan 《Linear and Multilinear Algebra》2018,66(12):2501-2511
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The article discusses the structure of cyclic semirings with noncommutative addition. In the infinite case, the addition is idempotent and is either left or right. Addition of a finite cyclic semirings can be either idempotent or nonidempotent. In the finite additively idempotent cyclic semiring, addition is reduced to the addition of a cyclic subsemiring with commutative addition and an absorbing element for multiplication and the addition of a cycle that is a finite semifield. 相似文献