On <em>C</em>-ideals and the basis of an ordered semigroup

Ze Gu; Xiang-Yun Xie; Jian Tang; Ze Gu; Xiang-Yun Xie; Jian Tang

doi:10.3934/math.2020245

AIMS Mathematics

2020, Volume 5, Issue 4: 3783-3790. doi: 10.3934/math.2020245

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Research article

On C-ideals and the basis of an ordered semigroup

1.
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing, Guangdong, P. R. China
2.
School of Mathematics and Computational Science, Wuyi University, Jiangmen, Guangdong, P. R. China
3.
School of Mathematics and Statistics, Fuyang Normal University, Fuyang, Anhui, P. R. China

Received: 26 February 2020 Accepted: 17 April 2020 Published: 21 April 2020
MSC : 06F05, 20M12

In this paper, we characterize ordered semigroups containing the greatest ideal and give the conditions of the greatest ideal being a C-ideal in an ordered semigroup. Moreover, we introduce the concept of a basis of an ordered semigroup and study the relationship between the greatest C-ideal and the basis in an ordered semigroup.
- ordered semigroup,
- greatest ideal,
- C-ideal,
- basis,
- greatest C-ideal
Citation: Ze Gu, Xiang-Yun Xie, Jian Tang. On C-ideals and the basis of an ordered semigroup[J]. AIMS Mathematics, 2020, 5(4): 3783-3790. doi: 10.3934/math.2020245

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Abstract

In this paper, we characterize ordered semigroups containing the greatest ideal and give the conditions of the greatest ideal being a C-ideal in an ordered semigroup. Moreover, we introduce the concept of a basis of an ordered semigroup and study the relationship between the greatest C-ideal and the basis in an ordered semigroup.

References

[1]	N. Kehayopulu, On weakly prime ideals in ordered semigroups, Math. Japon., 35 (1990), 1050-1056.
[2]	N. Kehayopulu, On prime, weakly prime ideals in ordered semigroups, Semigroup Forum, 44 (1992), 341-346. doi: 10.1007/BF02574353
[3]	N. Kehayopulu, On completely regular poe-semigroups, Math. Japon., 37 (1992), 123-130.
[4]	N. Kehayopulu, M. Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum, 65 (2002), 128-132. doi: 10.1007/s002330010079
[5]	N. Kehayopulu, M. Tsingelis, Fuzzy bi-ideals in ordered semigroups, Inform. Sci., 171 (2005), 13-28. doi: 10.1016/j.ins.2004.03.015
[6]	N. Kehayopulu, M. Tsingelis, Regular ordered semigroups in terms of fuzzy subsets, Inform. Sci., 176 (2006), 3675-3693. doi: 10.1016/j.ins.2006.02.004
[7]	X. Y. Xie, J. Tang, Fuzzy radicals and prime fuzzy ideals of ordered semigroups, Inform. Sci., 178 (2008), 4357-4374. doi: 10.1016/j.ins.2008.07.006
[8]	X. Y. Xie, J. Tang, Regular ordered semigroups and intra-regular ordered semigroups in tems of fuzzy subsets, Iranian J. Fuzzy Syst., 7 (2010), 121-140.
[9]	M. Shabir, A. Khan, Characterizations of ordered semigroups by the properties of their fuzzy ideals, Comput. Math. Appl., 59 (2010), 539-549. doi: 10.1016/j.camwa.2009.06.014
[10]	M. Shabir, A. Khan, Fuzzy quasi-ideals of ordered semigroups, Bull. Malays. Math. Sci. Soc, 34 (2011), 87-102.
[11]	I. Fabrici, Semigroups containing covered two-sided ideals, Math. Slovaca, 34 (1984), 355-363.
[12]	M. F. Wu, X. Y. Xie, On C-ideals of ordered semigroups, J. Wuyi University (in Chinese), 9 (1995), 43-46.
[13]	X. Y. Xie, M. F. Wu, On po-semigroups containing no maximal ideals, Southeast Asian Bull Math., 20 (1996), 31-36.
[14]	H. Y. Mao, X. Z. Xu, X. P. Lian, On C-ideals of ordered semigroups, J. Shandong University (in Chinese), 45 (2010), 14-16.
[15]	L. Fuchs, Partially Ordered Algebraic Systems, New York: Pregamon Press, 1963.
[16]	N. Kehayopulu, Note on Green's relations in ordered semigroups, Math. Japon., 36 (1991), 211-214.

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