JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (12): 46-53.doi: 10.6040/j.issn.1671-9352.0.2023.142

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Several classes of good congruences on r-wide semigroups

SHAO Lei, GONG Chunmei*   

  1. School of Science, Xian University of Architecture and Technology, Xian 710055, Shaanxi, China
  • Published:2024-12-12

Abstract: Several classes of good congruences on r-wide semigroups are characterized by(*,~)-Greens relations. It is showed that for r-wide semigroups, such as the least class of(left; right)regular bands-good congruence, the least class of(left; right)regular quasi-weakly adequate semigroups-good congruence and so on.

Key words: (*,~)-Greens relation, r-wide semigroup, good congruence

CLC Number: 

  • O152.7
[1] HOWIE J M. An introduction to semigroup theory[M]. London: Academic Press, 1967:116-117.
[2] FOUNTAIN J B. Abundant semigroups[J]. Proceeding of the London Mathematical Society, 1982, 44(1):103-129.
[3] LAWSON M V. Rees matrix semigroups[J]. Proceedings of the Edinburgh Mathematical Society, 1990, 33(1):23-37.
[4] GUO Yuqi, SHUM K P, GONG Chunmei. On(*,~)-Greens relations and ortho-lc-monoids[J]. Communincation in Algebra, 2011, 39(1):5-31.
[5] HALL T E. Congruences and Greens relations on regular semigroups[J]. Glasgow Mathematical Journal, 1972, 13(2):167-175.
[6] 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 Science Edition), 2000, 36(3):25-13.
[7] 郑娇. 几类弱适当半群的若干研究[D]. 西安:西安建筑科技大学, 2013. ZHENG Jiao. Some studies on several of weakly adequate semigroups[D]. Xian: Xian University of Architecture and Technology, 2013.
[8] GUO Yuqi, GONG Chunmei, KONG Xiangjun.(*,~)-Good congruences on regular ortho-lc-mon-oids[J]. Algebra Colloquium: Academy of Mathematics and Systems Science, 2014, 21(2):235-248.
[9] 宫春梅. G-广义完全正则半群的若干研究[D]. 重庆:西南大学, 2011. GONG Chunmei. Some stuties on G-generalized completely regular semigroups[D]. Chongqing: Southwest University, 2011.
[10] GUO Xiaojiang, LIU Aiqin. Congruences on abundant semigroups associated with Greens *-relations[J]. Period Math Hung 2017, 75(3):14-28.
[11] 冯丽霞. 超r-宽大半群的若干研究[D]. 西安:西安建筑科技大学, 2018. FENG Lixia. Some studies on super-r-wide semigroups[D]. Xian: Xian University of Architecture and Technology, 2018.
[12] YAMADA M. Orthodox semigroups whose idempotents satisfy a certain identity[J]. Semigroup Forum, 1973, 6(1):113-128.
[13] PETRICH M. Lectures in semigroups[M]. Berlin: Akademic Press, 1977: 379-383.
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