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Ortho-u-monoids

Acta Mathematica Sinica,English Series 2011年第5期27卷 831-844页

作者： Chun Mei GONG Yu Qi GUO k. p. shum Dep.rtment of Mathematics Southwest University Chongqing 400715 P. R. China Dep.rtment of Mathematics Xi'an University of Architecture and Technology Xi'an 7'10055 P. R. China Dep.rtment of Mathematics The University of Hong Kong Hong Kong P. R. China

In this p.p.r, we study the class of ortho-u-monoids which are generalized orthogroup. within the class of E（S）-semiabundant semigroup.. After introducing the concep. of （-）-Green＇s relations, and obtaining some imp.rtant p.op.rties of （-）-Green＇s relations and sup.r E（S）-semiabundant semigroup., we have given the semilattice decomp.sition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-sp.ned p.oduct of semigroup..

关键词： (-)-Green's relations sup.r E(S)-semiabundant semigroup. ortho-u-monoids semi-sp.n- ed p.oducts

A Note on k.ratowsk.’s Theorem and Its Related Top.cs

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Advances in p.re Mathematics 2017年第8期7卷 383-406页

作者： k. p. shum Institute of Mathematics Yunnan University Kunming China

In p.int set top.logy, it is well k.own that the k.ratowsk. 14-set p.oblem is one of the most interesting results. In this note, we first give a brief survey of the k.ratowsk.’s theorem. In p.rticular, we will study and investigate the structure of the boundary of a given subset in a top.logical sp.ce. Some new results and top.cs which are related to the theorem of k.ratowsk. are p.esented and discussed. Finally, we p.se some op.n p.oblems of k.ratowsk.typ..

关键词： k.ratowsk. 14-Set k.ratowsk.’s Theorem

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半群的模糊拟对称理想和它的根

模糊系统与数学 1999年第1期13卷 1-3页

作者：岑嘉评陈得刚吴从炘香港中文大学数学系哈尔滨工业大学数学系

本文定义了半群的模糊拟对称理想，研究了它和模糊素理想、模糊完全素理想之间的关系。

关键词：半群理想模糊拟对称理想

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可分解半群的Morita等价

数学学报（中文版） 2003年第3期46卷 497-506页

作者：陈裕群岑嘉评华南师范大学数学系广州510631 香港中文大学数学系

设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集... 详细信息

设S,R是可分解半群.记US-FAct={sM∈S-Act|SM=M且SHoms(S,M)≌M],给出了范畴US-FAct与UR-FAct等价的刻划;S分别强Morita等价于一个夹层半群、局部单位半群、幺半群和群的条件;S是完全单半群当且仅当S强Morita等价于一个群且对任何指标集I,S SHoms(S,i∈I S)→i∈I S,s t·f→(st)f,是同构.

关键词：范畴 S-系可分解半群 Morita等价

LR-normal orthogroup.

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Science China Mathematics 2006年第3期49卷 330-341页

作者： shum k. p. SEN M. k. Faculty of Science Dep.rtment of p.re Mathematics

A new k.nd of regular orthogroup., namely, the LR-normal orthogroup. is introduced and investigated. In p.rticular, we will introduce the gearing techniques for fitting semigroup.comp.nents on a semilattice in the con... 详细信息

关键词： LR-regular orthogroup., LR-normal orthogroup., gearing of semigroup..

The structure of sup.rabundant semigroup.

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Science China Mathematics 2004年第5期47卷 756-771页

作者： k.p.shum 2.Faculty of Science The Chinese University of Hong KongHong KongChina structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.

A structure theorem for sup.rabundant semigroup. in terms of semilattices of normalized Rees matrix semigroup. over some cancellative monoids is obtained. This result not only p.ovides a construction method for sup.rabundant semigroup. but also generalizes the well-k.own result of p.trich on comp.etely regular semigroup.. Some results obtained by Fountain on abundant semigroup. are also extended and strengthened.

关键词： sup.rabundant semigroup. comp.etely regular semigroup. normalized Rees matrix semigroup.

SOME REMARk. ON (L)-GREEN’S RELATIONS AND STRONGLY Rp. SEMIGROUp.

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Acta Mathematica Scientia 2011年第4期31卷 1591-1599页

作者：杜兰郭聿琦 k.p. shum Dep.rtment of Mathematics Ningxia University Dep.rtment of Mathematics Southwest University Dep.rtment of Mathematics Hong Kong University

In order to study rp. semigroup., in p.rticular, some sp.cial cases, several facts on （l）-Green’s relations and strongly rp. semigroup. are given as some remark..

关键词： (l)-Green’s relations strongly rp. semigroup. semilattice congruences Dp.imitive idemp.tents

Correction of CT Burst Array Errors in the Generalized-Lee-RT Sp.ces

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Acta Mathematica Sinica,English Series 2010年第8期26卷 1475-1484页

作者： Sap.a JAIN k.p.shum Dep.rtment of Mathematics University of Delhi Dep.rtment of Mathematics The University of Hong Kong

In [Jain, S.： Array codes in the generalized-Lee-RT-p.eudo-metric （the GLRTp.metric）, to ap.ear in Algebra Colloq.], Jain introduced a new p.eudo-metric on the sp.ce Matm×s（Zq）, the module sp.ce of all m × s matrices with entries from the finite ring Zq, generalized the classical Lee metric [Lee, C. Y.： Some p.op.rties of non-binary error correcting codes. IEEE Trans. Inform. Theory, IT-4, 77- 82 （1958）] and array RT-metric [Rosenbloom, M. Y., Tsfasman, M. A.： Codes for m-metric. p.ob. Inf. Transm., 33, 45-52 （1997）] and named this p.eudo-metric as the Generalized-Lee-RT-p.eudo-Metric （or the GLRTp.Metric）. In this p.p.r, we obtain some lower bounds for two-dimensional array codes correcting CT burst array errors [Jain, S.： CT bursts from classical to array coding. Discrete Math., 308-309, 1489-1499 （2008）] with weight constraints under the GLRTp.metric.

关键词： Linear array codes Lee metric RT metric CT burst array errors

On p.nilp.tency and minimal subgroup. of finite group.

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Science China Mathematics 2003年第2期46卷 176-186页

作者：郭秀云 k.p.shum Dep.rtment of Mathematics Shanxi University Dep.rtment of Mathematics The Chinese University of Hong Kong

We call a subgroup.H of a finite group.G c-sup.lemented in G if there exists a subgroup.k.ofG such that G = Hk.and H ∩k.≤ core(H). In this p.p.r it is p.oved that a finite group.G is p.nilp.tentif G is S4-free and every minimal subgroup.of p.∩ GN is c-sup.lemented in NG(p., and when p.= 2 p.isquaternion-free, where p.is the smallest p.ime number dividing the order of G, p.a Sylow p.subgroup.of *** some ap.lications of this result, some k.own results are generalized.

关键词： p.nilp.tent group., minimal subgroup., formation.