共查询到19条相似文献,搜索用时 593 毫秒
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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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研究了完全正则半环的特征.利用半群的方法,得到了当分配半环的乘法幂等元集分别是左零带、矩形带以及正规带时,该类半环成为完全正则半环的等价刻画,推广并改进了相关文献的主要结果. 相似文献
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半环半直积的同构定理 总被引:1,自引:0,他引:1
谢蓓蓓 《纯粹数学与应用数学》2004,20(4):364-367
半群半直积及封闭性刻划于文[1],为将半直积的研究推广至半环中,本文首先在交换半环与交换半群的直积上定义加法及乘法运算,从而构造了一类半环;半环半直积.并讨论了半环半直积的同构等问题. 相似文献
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首先给出了由半环的乘法半群上的格林关系所确定的半环开同余的性质和刻画.其次,由开同余出发,得到了六个不同的半环类,并证明了这六个半环类均是半环簇.最后,对半环簇的子簇格上的开算子进行了探讨,得到了一些有趣的结果. 相似文献
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幂等元半环簇和幂等元分配半环簇依次记为I,ID.满足附加恒等式xyx x xyx=xyx的幂等元半环簇的子簇记为P.本文主要刻划了P中成员的一些性质,并对P∩ID中的部分成员进行了次直积分解. 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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练利锋 《纯粹数学与应用数学》2018,(1):81-85
首先给出了加法半群是带,乘法半群是完全正则半群的半环上的格林关系所确定的开同余的刻画,并对其相关性质做了一定的探讨,最后证明了CR(n,1)中半环上的S/L°,S/R°分别是左、右约简的. 相似文献
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张娟娟 《纯粹数学与应用数学》2009,25(4):716-720
假设S是乘法半群为完全正则半群的半环.给出了S上的Green关系H,L和D是S上的半环同余的等价刻划,并利用幂等元的方法证明了在一定条件下D是S上的同余当且仅当L,R是S上的同余. 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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研究了加法半群为半格,乘法半群为左正规纯正群的半环.证明了此类半环(S,+,.)可以嵌入到半格(S,+)的自同态半环中.构造S的一个特定的偏序关系,得到了(S,·)上的自然偏序与所构造偏序相等的等价条件. 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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Semigroup Forum - In this paper, by means of congruence openings of multiplicative Green’s relations on a semiring we define and study several varieties of semirings, obtain the relationship... 相似文献
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Ordered bands are regarded as semirings whose multiplicative reduct is a band and whose additive reduct is a chain. We find
the variety of semirings generated by all ordered bands and we determine part of the lattice of its subvarieties. 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 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. 相似文献
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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
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In a series of papers, Green’s relations on the additive and multiplicative reducts of a semiring proved to be a very useful
tool in the study of semirings. However, in the vast majority of cases, Green’s relations are not congruences, and we show
that in such cases it is much more convenient to use the congruence openings of Green’s relations, instead of the Green’s
relations themselves. By means of these congruence openings we define and study several very interesting operators on the
lattices of varieties of semirings and additively idempotent semirings, and, in particular, we establish order embeddings
of the lattice of varieties of additively idempotent semirings into the direct products of the lattices of open (resp. closed)
varieties with respect to two opening (resp. closure) operators on this lattice that we introduced. 相似文献