共查询到19条相似文献,搜索用时 578 毫秒
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首先讨论逆半群Sa的半上的自然偏序与各Sa上的自然偏序之间的关系,然后讨论逆半群Sa的半格S的幂等元集Ea的闭包限制在Sa上与Ea的闭包的关系. 相似文献
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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. 相似文献
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利用自由含幺半群X*上的一个偏序关系,介绍了一类特殊的后缀码.通过定义这类后缀码上的两种二元运算,研究了这类后缀码的代数性质.证明了该子类在这两种运算下形成一个加法导出是半格的半环,并且满足吸收律.从而提供了一个满足吸收律的半格序半群的例子. 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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本文研究了完全正则半群簇的子簇格[V+∩PV,V+∩PV]的某些格运算性质,我们证明了簇V+∩PV可分解为V与V+∩PV的并;对任意完全正则半群簇W,有W∩(V∨V+∩PV)=(W∩V)∨(W∩V+∩PV).特别地,我们得到了等式V+∩PV=V成立的若干条件. 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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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
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F. Pastijn 《Semigroup Forum》1983,26(1):151-166
In [2] it is shown that every idempotent distributive semiring is the P?onka sum of a semilattice ordered system of idempotent distributive semirings which satisfy the generalized absorption law x+xyx+x=x. We shall show that an idempotent distributive semiring which satisfies the above absorption law must be a subdirect product of a distributive lattice and a semiring which satisfies the additional identity xyx+x+xyx=xyx. Using this, we construct the lattice of all equational classes of idempotent distributive semirings for which the two reducts are normal bands. 相似文献
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An ordered semiring is a semiring S equipped with a partial order ≤ such that the operations are monotonic and constant 0 is the least element of S.In this paper,several notions,for example,ordered ideal,minimal ideal,and maximal ideal of an ordered semiring,simple ordered semirings,etc.,are introduced.Some properties of them are given and characterizations for minimal ideals are established.Also,the matrix semiring over an ordered semiring is consid-ered.Partial results obtained in this paper are analogous to the corresponding ones on ordered semigroups,and on the matrix semiring over a semiring. 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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设R是含有恒等元1的半环,C是R上的中心子半环.Tn(R)是R上的n阶上三角矩阵C-代数.证明了当R是一个幂等元都是中心元的半环时,映射Φ:Tn(R)→Tn(R)是乘法半群自同构当且仅当存在Tn(R)中的可逆矩阵G和R中的半环自同构τ使得A=(aij)n×n∈Tn(R),均有Φ(A)=G-1τ(A)G.这里τ(A)=(τ(aij))n×n,n2. 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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Yi-Jia Tan 《Linear and Multilinear Algebra》2018,66(12):2501-2511