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| The extension on cancellative partial order and quotient ordered homomorphism of cancellative partially ordered semigroup |
| SHAO Haiqin, GUO Liqin |
| School of Mathematics and Statistics Institute, Tianshui Normal University, Tianshui 741001, Gansu Province, China |
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Abstract This paper studies the cancellative partial ordered extension and properties of quotient ordered homomorphisms of cancellative partially ordered semigroups(CPOS). The notion on quotient semi-pseudoorder of partially ordered semigroup(POS) is introduced. With the quotient semi-pseudoorder of CPOS and using the method of partial ordered extension of POS, the sufficient condition for extending a cancellative partial order of CPOS to another cancellative partial order is derived. It is also shown that quotient ordered homomorphism of partially ordered semigroup POS can be depicted by semi-pseudoorder σ, closed semi-pseudochain of modulo σ, quotient semi-pseudoorder, partial ordered extension of partially ordered semigroup, and cancellative partial ordered extension of CPOS. Some important conclusions are obtained.
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Received: 20 October 2014
Published: 01 May 2016
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Cite this article:
SHAO Haiqin, GUO Liqin. The extension on cancellative partial order and quotient ordered homomorphism of cancellative partially ordered semigroup. Journal of Zhejiang University (Science Edition), 2016, 43(5): 512-516.
URL:
https://www.zjujournals.com/sci/EN/Y2016/V43/I5/512
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可消偏序半群的可消偏序扩张与商序同态
引入偏序半群的商半拟序的概念，利用商半拟序给出了可消偏序半群上的偏序可扩张为可消偏序的充分条件.通过偏序半群的半拟序σ、模σ的闭半拟链，商半拟序和偏序扩张以及可消偏序半群的可消偏序扩张，对偏序半群的商序同态进行了刻画，得到了若干重要的结论.
关键词：
可消偏序半群,
半拟序,
商半拟序,
闭半拟链,
偏序扩张,
可消偏序扩张,
商序同态
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[1] 谢湘云.序半群引论[M].北京:科学出版社,2001:1-67. XIE Xiangyun. An Introduction to Ordered Semigroups Theory[M]. Beijing: Science Press,2001:1-67.
[2] 邵海琴,薛占军,雷振亚.偏序半群的偏序扩张[J].纯粹数学与应用数学,2008,24(4):730-736. SHAO Haiqin, XUE Zhanjun, LEI Zhenya. The extension on partial order of partially ordered semigroups[J]. Pure and Applied Mathematics,2008,24(4):730-736.
[3] CAO Y L. Quotient ordered homomorphisms of ordered semigroups[J]. Communications in Algebra,2003,31:5563-5579.
[4] XIE X Y . An extension of partial orders of commutative partially ordered semigroups[J]. Journal of Mathematical Research and Exposition,2005,25(4):676-682.
[5] NAKADA O. Partially ordered Ablian semigroups I[J]. J Fac Sct Hokkaido Univ,1951,11:181-189.
[6] NAKADA O. Partially ordered Ablian semigroups II[J]. J Fac Sct Hokkaido Univ,1952,12:73-86.
[7] HULIN A J. Extensions of ordered semigroups[J]. Semigroups Forum,1971(2):336-342.
[8] HULIN A J. Extensions of ordered semigroups[J]. Czech Math J,1976,26:1-12.
[9] 邵海琴.偏序半环的偏序扩张[J].宁夏大学学报:自然科学版,2007,28(4):293-296. SHAO Haiqin. The extension on partial order of partially ordered semirings[J]. Journal of Ningxia University: Natural Science Edition,2007,28(4):293-296.
[10] 邵海琴,何万生,杨随义,等.偏序半群的同态和商序同态的若干重要性质[J].兰州理工大学学报,2011,37(5):137-141. SHAO Haiqin, HE Wansheng, YANG Suiyi, et al. Some important properties on homomorphisms and quotient ordered homomorphisms of partially ordered semigroups[J]. Journal of Lanzhou University of Technology,2011,37(5):137-141.
[11] 邵海琴,何万生,郭莉琴,等.可换偏序半群的同态和商序同态的若干重要性质[J].浙江大学学报:理学版,2013,40(4):367-370. SHAO Haiqin, HE Wansheng, GUO Liqin, et al. Some important properties on homomorphisms and quotient ordered homomorphisms of commutative partially ordered semigroups[J]. Journal of Zhejiang University: Science Edition,2013,40(4):367-370.
[12] CAO Y L. Decompositions and pseudo-orders of ordered semigroups[J]. Semigroups Forum,2004,68:177-185.
[13] 邵海琴,何万生,郭莉琴.偏序半群的半拟序、正则同余与商序同态[J].宁夏大学学报:自然科学版,2015, 36(2):109-114. SHAO Haiqin, HE Wansheng, GUO Liqin. Semi-pseudoorder, regular congruence and quotient ordered homomorphism of partially ordered semigroups[J]. Journal of Ningxia University: Natural Science Edition,2015,36(2):109-114. |
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