JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (6): 6-12.doi: 10.6040/j.issn.1671-9352.0.2023.045

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Good congruences on r-wide semigroups whose idempotents form normal band

Chunmei GONG(),Jiao PENG*(),Xuena bai   

  1. School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, Shaanxi, China
  • Received:2023-02-14 Online:2024-06-20 Published:2024-06-17
  • Contact: Jiao PENG E-mail:meigongchu@163.com;pengjiaoyx@163.com

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Abstract:

The definition of good congruence pairs is established by means of quasi-spined product structure of r-wide semigroups whose idempotents form normal band, and then, any good congruences of r-wide semigroups whose idempotents form normal band are characterized by using the good congruence pairs.

Key words: r-wide semigroup, normal band, good congruence, good congruence pair

CLC Number: 

  • O152.7
1 GUO Y Q , SHUM K P , GONG C M . On (*, ~)-Greens relations and ortho-lc-monoids[J]. Communications in Algebra, 2010, 39 (1): 5- 31.
doi: 10.1080/00927870903428247
2 彭娇, 宫春梅. 幂等元集为正规带的r-宽大半群[J]. 云南大学学报(自然科学版), 2022, 44 (5): 895- 901.
PENG Jiao , GONG Chunmei . r-wide semigroups whose idempotents form normal band[J]. Journal of Yunnan University (Natural Sciences Edition), 2022, 44 (5): 895- 901.
3 郑娇, 任学明. 弱适当半群的研究[J]. 江南大学学报(自然科学版), 2013, 12 (1): 97- 100.
ZHENG Jiao , REN Xueming . Studies on weakly adequate semigroups[J]. Journal of Jiangnan University(Natural Science Edition), 2013, 12 (1): 97- 100.
4 罗彦锋, 赵华, 郭小江. 幂等元满足置换恒等式的半群上的好同余[J]. 兰州大学学报(自然科学版), 2000, 36 (3): 25- 31.
LUO Yanfeng , ZHAO Hua , GUO Xiaojiang . Good congruences on abundant semigroups whose idempotents satisfy permutation identities[J]. Journal of Lanzhou University (Natural Sciences), 2000, 36 (3): 25- 31.
5 LUO Yanfeng , GUO Xiaojiang . Good congruences on a type σ semigroup[J]. Communications in Algebra, 1999, 27 (12): 6199- 6211.
doi: 10.1080/00927879908826817
6 ZHANG Tianjie , TIAN Zhenji , SHI Yabing . Good congruences on abundant semigroups with PSQ-adequate transversals[J]. Semigroup Forum, 2014, 89 (2): 462- 468.
doi: 10.1007/s00233-014-9584-1
7 GONG Chunmei , REN Xueming , YUAN Ying . The (*, ~)-good congruences on normal ortho-lc-monoids[J]. Advances in Mathematics, 2015, 44 (3): 369- 378.
8 HOWIE J M . Fundamentals of semigroup theory[M]. Oxford: Clarendon, 1995.
9 LAWSON M V . The natural partial order on an abundant semigroup[J]. Proceedings of the Edinburgh Mathematical Society, 1987, 30 (2): 169- 186.
doi: 10.1017/S001309150002825X
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