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A Characterization of Metahomomorphisms on abelian groups

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Northeastern Mathematical Journal 2006年第4期22卷 383-386页

作者：丁龙云顾沛 School of Mathematical Sciences and LPMC Nankai UniversityTianjin300071

In this paper, a characterization of metahomomorphisms on abelian groups is given.

关键词： metahomomorphism on group abelian group Yang-Baxter equation

Structure of abelian rings

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Frontiers of Mathematics in China 2017年第1期12卷 117-134页

作者： Juncheol HAN Yang LEE Sangwon PARK Department of Mathematics Education Pusan National University Pusan 46241 Korea Department of Mathematics Dong-A University~ Pusan 49315 Korea

Let R be a ring with identity. We use J（R）, G（R）, and X（R） to denote the Jacobson radical, the group of all units, and the set of all nonzero nonunits in R, respectively. A ring is said to be abelian if every idempotent is central. It is shown, for an abelian ring R and an idempotent-lifting ideal N J（R） of R, that H has a complete set of primitive idempotents if and only if R/N has a complete set of primitive idempotents. The structure of an abelian ring R is completely determined in relation with the local property when X（R） is a union of 2, 3, 4, and 5 orbits under the left regular action on X（R） by G（R）. For a semiperfect ring R which is not local, it is shown that if G（R） is a cyclic group with 2 ∈ G（R）, then R is finite. We lastly consider two sorts of conditions for G（R） to be an abelian group.

关键词： abelian ring regular group action local ring semiperfect ring finite ring abelian group idempotent-lifting complete set of primitive idempotents

SOME NEW FAMILIES OF SDSS AND HADAMARD MATRICES

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Acta Mathematica Scientia 1996年第2期16卷 153-161页

作者：夏明远 Dept. of Math. Huazhong Normal Univ. Wuhan 430070 China

In this paper we prove that for any prime power q equivalent to 3 (mod 8) there exist 4 - {q(2); k, k, k, k; lambda} supplementary difference sets (SDSs) with k = q(q - 1)/2, lambda 4k - q(2), and Hadamard matrices of order 4q(2), and give several constructions of these SDSs. Moreover, combining the results of reference [1], we conclude that for any prime p equivalent to 3 (mod 8) and integer r greater than or equal to 1 there exists an Hadamard matrix of order 4p(2r).

关键词： abelian group finite field supplementary difference sets Hadamard matrix

On Weakly Semi-radicable groups

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Northeastern Mathematical Journal 2005年第2期21卷 181-188页

作者：吕恒段泽勇余大鹏 College of Mathematics and Information Science Shanxi Normal University Xi'an 710062Department of Mathematics Southwest China Normal University Chongqing 400715 Department of Mathematics Southwest China Normal University Chongqing 400715 Department of Mathematics Yuxi College Yongchuan Chongqing 402168

In this paper, we prove that if a torsion nilpotent group G is a weak semi-radicable group, then every Sylow p-group Gp is a central-by-finite p-group, and moreover Gp's center ζ(GP) satisfies |ζ(GP) : (ζ(GP))P| <... 详细信息

关键词： divisible group abelian group nilpotent group radicable group semiradicable group

Splitting Extensions of abelian by Hyper-(cyclic or finite) groups (Ⅱ)

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Journal of Southwest Jiaotong University(English Edition) 2006年第3期14卷 291-294页

作者：秦应兵 Department of Mathematics Southwest Jiaotong University Chengdu 610031 China

Let F be a locally defined formation consisting of locally solvable groups, G a hyper-（ cyclic or finite） locally solvable group and A a noetherian ZG-module with all irreducible ZG-factors being finite. The following conclusion is obtained： if G∈F, f（ ∞ ） include f（p）, f（p） ≠φ for each p∈π, and A has no nonzero F central ZG- images, then any extension E of A by G splits conjugately over A, and A has no nonzero F central ZG-factors.

关键词： Noetherian module abelian group Hyper-(cyclic or finite) group Splitting conjugacy Extension