共查询到17条相似文献,搜索用时 78 毫秒
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将Green关系推广到Green~-关系。给出了密码■-富足半群的半格分解,利用此分解,证明了■-富足半群为正规密码■-富足半群当且仅当它是完全■-单半群的强半格. 相似文献
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证明了H~#-富足半群S是正规密码H~#-富足半群当且仅当它是完全J~#-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广. 相似文献
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证明了ο-超富足半群S是正规密码ο-超富足半群当且仅当它是完全Jο-单半群的强半格.该结果也是正规密码超富足半群和正规密码群并半群分别在超富足半群和完全正则半群上的相应结构定理的推广。 相似文献
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弱交换富足序半群(Ⅰ) 总被引:5,自引:0,他引:5
本文将序半群上的 Green’s-关系推广为 Green’s*一关系.给出主序(左、右)*-理想、主序*-滤特征描述和弱交换富足序半群的特征.用这些特征证明了一类弱交换富足序半群的结构定理:若序半群S满足 ,则S是弱交换富足序半群当且仅当S是左(右)单序半群{(e)(S)}的半格. 相似文献
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推广了半群的强半格分解的定义,得到了半群的拟强半格分解,并证明了完全正则半群为群 的正则(或右拟正规)带当且仅当它是完全单半群的拟强半格(且 )). 相似文献
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富足半群上的自然偏序 总被引:4,自引:0,他引:4
本文研究富足半群上的自然偏序,得到Green关系和自然偏序之间的联系,确定了富足半群何时关于自然偏序具有单边(双边)相容,另外,也研究了富足半群的本原元。 相似文献
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《代数通讯》2013,41(6):2461-2479
Superabundant semigroups are generalizations of completely regular semigroups written the class of abundant semigroups. It has been shown by Fountain that an abundant semigroup is superabundant if and only if it is a semilattice of completely J *-simple semigroups. Reilly and Petrich called a semigroup S cryptic if the Green's relation H is a congruence on S. In this paper, we call a superabundant semigroup S a regular crypto semigroup if H * is a congruence on S such that S/H * is a regular band. It will be proved that a superabundant semigroup S is a regular crypto semigroup if and only if S is a refined semilattice of completely J *-simple semigroups. Thus, regular crypto semigroups are generalization of the cryptic semigroups as well as abundant semigroups. 相似文献
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We characterize the ordered semigroups which are decomposable into simple and regular components. We prove that each ordered semigroup which is both regular and intra-regular is decomposable into simple and regular semigroups, and the converse statement also holds. We also prove that an ordered semigroup S is both regular and intra-regular if and only if every bi-ideal of S is an intra-regular (resp. semisimple) subsemigroup of S. An ordered semigroup S is both regular and intra-regular if and only if the left (resp. right) ideals of S are right (resp. left) quasi-regular subsemigroups of S. We characterize the chains of simple and regular semigroups, and we prove that S is a complete semilattice of simple and regular semigroups if and only if S is a semilattice of simple and regular semigroups. While a semigroup which is both π-regular and intra-regular is a semilattice of simple and regular semigroups, this does not hold in ordered semigroups, in general. 相似文献
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推广了著名的Petrich的完全正则半群为群的正规带当且仅当它为完全单半群的强半格的结果,证明了完全正则半群为群的正则(或右拟正规)带当且仅当它是完全单半群的HG(LG)-强半格. 相似文献
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S为半群,如果S中的每个Lρ-类都含幂等元,称S为Lρ-富足半群.特别地,如果对任意的α∈S,集合Iα∩Lα^ρ都只含唯一的元素,称S为强Lρ-富足半群.在S上通过一个非恒等置换σ,给出了PI-强Lρ-富足半群的结构定理. 相似文献
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Ernie Manes 《Semigroup Forum》2006,72(1):94-120
The variety of guarded semigroups consists of all (S,·, ˉ) where (S,·) is a semigroup and x ↦ \overline{x} is a unary operation
subject to four additional equations relating it to multiplication. The semigroup Pfn(X) of all partial transformations on
X is a guarded semigroup if x \overline{f} = x when xf is defined and is undefined otherwise. Every guarded semigroup is
a subalgebra of Pfn(X) for some X. A covering theorem of McAlister type is obtained. Free guarded semigroups are constructed
paralleling Scheiblich's construction of free inverse semigroups. The variety of banded semigroups has the same signature
but different equations. There is a canonical forgetful functor from guarded semigroups to banded semigroups. A semigroup
underlies a banded semigroup if and only if it is a split strong semilattice of right zero semigroups. Each banded semigroup
S contains a canonical subsemilattice g⋆(S). For any given semilattice L, a construction to synthesize the general banded semigroup S with g⋆ ≅ L is obtained. 相似文献
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We study the decomposition of left regular ordered semigroups into left regular components and the decomposition of intra-regular ordered semigroups into simple or intra-regular components, adding some additional information to the results considered in [KEHAYOPULU, N.: On left regular ordered semigroups, Math. Japon. 35 (1990), 1057–1060] and [KEHAYOPULU, N.: On intra-regular ordered semigroups, Semigroup Forum 46 (1993), 271–278]. We prove that an ordered semigroup S is left regular if and only if it is a semilattice (or a complete semilattice) of left regular semigroups, equivalently, it is a union of left regular subsemigroups of S. Moreover, S is left regular if and only if it is a union of pairwise disjoint left regular subsemigroups of S. The right analog also holds. The same result is true if we replace the words “left regular” by “intraregular”. Moreover, an ordered semigroup is intra-regular if and only if it is a semilattice (or a complete semilattice) of simple semigroups. On the other hand, if an ordered semigroup is a semilattice (or a complete semilattice) of left simple semigroups, then it is left regular, but the converse statement does not hold in general. Illustrative examples are given. 相似文献
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