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SOME REMARkS ON (L)-GREEN’S RELATIONS AND STRONGLY Rpp SEMIGROUpS

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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 Department of Mathematics Ningxia University Department of Mathematics Southwest University Department of Mathematics Hong Kong University

In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.

关键词： (l)-Green’s relations strongly rpp semigroups semilattice congruences Dprimitive idempotents

U-Concordant Semigroups

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Algebra Colloquium 2018年第2期25卷 295-318页

作者： Xueming Ren Yanhui Wang k.p. shum Department of Mathematics Xi'an University of Architecture and Technology Xi'an 710055 China College of Mathematics and Systems Science Shandong University of Science and Technology Qingdao Shandong 266590 China Institute of Mathematics Yunnan University Kunming 650091 China

We introduce the relations Lu and Ru with respect to a subset U of idempotents. Based on Lv and Rv, we define a new class of semigroups which we name U-concordant semigroups. Our purpose is to describe U-concordant semigroups by generalized categories over a regular biordered set. We show that the category of U-concordant semigroups and admissible morphisms is isomorphic to the category of RBS generalized categories and pseudo functors. Our approach is inspired from Armstrong＇s work on the connection between regular biordered sets and concordant semigroups. The significant difference in strategy is by using RBS generalized categories equipped with pre-orders, we have no need to discuss the quotient of a category factored by a congruence.

关键词： regular semigroup regular biordered set RBS generalized category RBS generalized groupoid concordant semigroup

On Ordered rpp Semigroups with Max-idempotents

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Algebra Colloquium 2015年第1期22卷 11-22页

作者： Xiaojiang Guo Chenchen Ren k.p. shum Department of Mathematics Jiangxi Normal University Nanchang Jiangxi 330022 China Institute of Mathematics Yunnan University Kunming Yunnan 650091 China

In this paper, we establish a structure theorem of naturally ordered rpp semigroups with max-idempotents. Results on naturally ordered semigroups with max- idempotents in the literature are extended and amplified. Some previous results obtained by Blyth, McFadden, Cuo and Xie on regular and abundant ordered semigroups are ex- tended to ordered roo semigrouos.

关键词： naturally ordered semigroup rpp semigroup greatest inverse maximal idem-potent

A Hua-like Theorem in Semirings＊

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Algebra Colloquium 2015年第3期22卷 445-448页

作者： Jun pei Yuqi Guo k.p. shum School of Mathematics and Statistics Lanzhou University Lanzhou 730000 China School of Mathematics and Statistics Southwest University Chongqing 400715 China Institute of Mathematics Yunnan University Kunming 650091 China

In this paper, we establish a Hua-Like theorem in some kind of semirings. This can be regarded as a generalized version of Hua＇s theorem from rings to semirings.

关键词： semiring Hua's theorem Hua-like theorem

The structure of superabundant semigroups

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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 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.

关键词： superabundant semigroups completely regular semigroups normalized Rees matrix semigroups

Correction of CT Burst Array Errors in the Generalized-Lee-RT Spaces

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

作者： Sapna JAIN k.p.shum Department of Mathematics University of Delhi Department of Mathematics The University of Hong Kong

In [Jain, S.： Array codes in the generalized-Lee-RT-pseudo-metric （the GLRTp-metric）, to appear in Algebra Colloq.], Jain introduced a new pseudo-metric on the space Matm×s（Zq）, the module space of all m × s matrices with entries from the finite ring Zq, generalized the classical Lee metric [Lee, C. Y.： Some properties 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. prob. Inf. Transm., 33, 45-52 （1997）] and named this pseudo-metric as the Generalized-Lee-RT-pseudo-Metric （or the GLRTp-Metric）. In this paper, 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-nilpotency and minimal subgroups of finite groups

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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 Department of Mathematics Shanxi University Department of Mathematics The Chinese University of Hong Kong

We call a subgroup H of a finite group G c-supplemented in G if there exists a subgroup k ofG such that G = Hk and H ∩k ≤ core(H). In this paper it is proved that a finite group G is p-nilpotentif G is S4-free and every minimal subgroup of p ∩ GN is c-supplemented in NG(p), and when p = 2 p isquaternion-free, where p is the smallest prime number dividing the order of G, p a Sylow p-subgroup of *** some applications of this result, some known results are generalized.

关键词： p-nilpotent groups, minimal subgroups, formation.

On Almost Armendariz Ring

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Algebra Colloquium 2020年第2期27卷 199-212页

作者： Om prakash Sushma Singh k.p.shum Department of Mathematics Indian Institute of Technology Patna PatnaBihar 801106India Department of Mathematics John Fulton Center The Chinese University of Hong KongShatinN.T.Hong KongChina

In this paper,we introduce the notion of an almost Armendariz ring,which is a generalization of an Armendariz ring,and discuss some of its *** has been found that every almost Armendariz ring is weak Armendariz but the converse is not *** prove that a ring R is almost Armendariz if and only if R[x]is almost *** is also shown th at if R/I is an almost Armendariz ring and I is a semicommutative ideal,then H is an almost Armendariz ***,the class of minimal non-commutative almost Armendariz rings is completely determined,up to isomorphism(minimal means having smallest cardinality).

关键词： Armendariz ring almost Armendariz ring weak Armendariz ring lower nil radical reduced ring semicommutative ring

On f-Disjunctive Languages, f-Disjunctive Domains and Solid Codes(Dedicated to the late professor Xu Yonghua (1932-2019))

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Algebra Colloquium 2020年第2期27卷 331-342页

作者： Jing Leng Yuqi Guo k.p.shum School of Mathematics and Statistics Lanzhou University Lanzhou 730000China Institute of Mathematics Yunnan University Kunming 650091China

Every language is either the disjoint union or the intersection of two disjunctive *** family of f-disjunctive languages is a natural generalization of the family of disjunctive *** domains(f-disjunctive domains)are defined as the languages which can be checked whether a given language is disjunctive(f-disjunctive)or *** f-disjunctive domains were first studied by Guo et *** *** continue their study on f-disjunctive *** new results for f-disjunctive domains,containing a relation between disjunctive domains and f-disjunctive domains,are *** this respect,we also make an appropriate opening for the completely dense languages and solid codes.

关键词： f-disjunctive languages f-disjunctive domains completely dense languages solid codes