[1]秦松,甘爱萍.加法半群为半格的半环上Green-关系[J].江西师范大学学报(自然科学版),2012,(02):151-154.
　QIN Song,GAN Ai-ping.The Green's Relations on a Semiring with Additive Semigroup as Semilattice[J].Journal of Jiangxi Normal University:Natural Science Edition,2012,(02):151-154.
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加法半群为半格的半环上Green-关系()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年02期
页码:
151-154
栏目:
出版日期:
2012-03-01

文章信息/Info

Title:
The Green's Relations on a Semiring with Additive Semigroup as Semilattice
作者:
秦松;甘爱萍
江西师范大学数学与信息科学学院,江西南昌,330022
Author(s):
QIN Song；GAN Ai-ping
关键词:
Green-关系; 半环; 理想; k-集
Keywords:
Green's relations;  semiring;  ideal;  -set
分类号:
O153.3；O152.7
文献标志码:
A
摘要:
利用半群代数理论研究了加法半群为半格的半环上的4种不同类型的Green-关系,并对它们的特征进行了刻画,证明了在加法半群为半格的半环上(f)=(f)且(n)=(n).
Abstract:
Four different kinds of Green's relations on a semiring with additive semigroup as semilattice is studied by the algebraic theory of semigroups. Some characterizations of these Green's relations are given. Also, it is shown that and on such a semiring.

参考文献/References:

[1] Howie J M. Fundametals of semigroups theory [M]. Oxford: Clarendon Press, 1995.
[2] Ciric M, Bogdanovic S. Semilattice decompositions of semigroups [J]. Semigroup Forum, 1996, 52(1): 119-132.
[3] 陈忠, 汪立民. 双单ω-半群同余格上的关系K [J]. 江西师范大学学报: 自然科学版, 2010, 34(2): 188-191.
[4] 郭爱丽, 朱用文. 正则矩阵半群中的格林关系 [J]. 山东科学, 2010, 23(4): 1-4.
[5] 包强, 梅永刚, 邵海琴. 半环上的Green's-L关系 [J]. 科学技术与工程, 2007, 7(7): 1416-1418.
[6] 平静水, 邓科峰. 幂等元半环上的D∨D关系 [J]. 安徽大学学报: 自然科学版, 2007, 31(1): 9-11.
[7] 张娟娟. 某些半环上Green关系的刻划 [J]. 纯粹数学与应用数学, 2009, 25(4): 716-720.
[8] Grillet M P. Green's relations in a semiring [J]. Portugal Math, 1970, 29 (4): 181-195.
[9] Bhuniya A K, Mondal T K. Distributive lattice decompositions of semirings with a semilattice additive reduct [J]. Semigroup Forum, 2010, 80(2): 293-301.
[10] Sen M K, Bhuniya A K. On additive idempotent k-regular semirings [J]. Bull Cal Math Soc, 2001, 93(5): 371-384.
[11] Kehayopulu N. Note on Green's relations in ordered semigroups [J]. Mathematica Japonica, 1991, 36(2): 211-214.
[12] Kehayopulu N. Ideals and green's relations in ordered semigroups [J]. International Journal of Mathematics and Mathematical Sciences, 2006(1): 1-8.
[13] Kehayopulu N, Tsingelis M. On left regular ordered semigroups [J]. Southeast Asian Bulletin of Mathematics, 2002, 25(4): 609-615.
[14] Burris S N, Sankappanavar H P. A course in universal algebra [M]. New York: Springer-Verlag, 1981.
[15] 陈培慈. 半环理论与语言和自动机 [M]. 南昌: 江西高校出版社, 1993.

备注/Memo

备注/Memo:
江西省自然科学基金(2010GZS0093)
更新日期/Last Update: 1900-01-01