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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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求证具有强半格结构的完全正则半群成为P-完全正则半群的充分条件.利用半群的强半格结构以及同余的性质.完全单半群的强半格-正规群带是P-完全正则半群.矩形群的强半格正规纯正群类ONBG,左群的强半格左正规纯整群类LONBG,群的强半格Clifford半群类,矩形带的强半格正规带类NB,都具有性质P. 相似文献
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本文研究了正则带的结构问题.利用拟强半格分解方法,获得了带为正则带当且仅当它为矩形带的拟强半格,推广了Yamada和Kimura关于正规带是矩形带的强半格的结果. 相似文献
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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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将Green关系推广到Green~-关系。给出了密码^ ~ H-富足半群的半格分解,利用此分解,证明了^ ~ H-富足半群为正规密码^H-富足半群当且仅当它是完全^ ~ H-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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本文利用半群研究中的同余方法,刻划了拟完全纯整半群的特征和结构。在若干准备之后,分别讨论了拟完全纯整半群上的半格同余和矩阵同余,在此基础上建立了拟完全纯整半群到拟群的所谓半格(矩阵)-矩阵(半格)分解,且给出了在纯整半群上的完整的推论,最后,还就拟群的特征和结构作了专门的讨论。 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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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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本文研究了左$C$-wrpp半群的加细半格结构,证明了左$C$-wrpp半群是左-${\cal R}$可消带的加细半格当且仅当它是一个$C$-wrpp半群和一个左正则带的织积. 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