### ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS

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Kong, Xiangjun;Wang, Pei

• 투고 : 2010.01.11
• 발행 : 2011.01.31
• 18 5

#### 초록

In this paper, the connection of the inverse transversal with the adequate transversal is explored. It is proved that if S is an abundant semigroup with an adequate transversal $S^o$, then S is regular if and only if $S^o$ is an inverse semigroup. It is also shown that adequate transversals of a regular semigroup are just its inverse transversals. By means of a quasi-adequate semigroup and a right normal band, we construct an abundant semigroup containing a quasi-ideal S-adequate transversal and conversely, every such a semigroup can be constructed in this manner. It is simpler than the construction of Guo and Shum [9] through an SQ-system and the construction of El-Qallali [5] by W(E, S).

#### 참고문헌

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#### 피인용 문헌

1. 1. CONGRUENCES ON ABUNDANT SEMIGROUPS WITH QUASI-IDEAL S-ADEQUATE TRANSVERSALS vol.29, pp.1, 2014, doi:10.4134/CKMS.2011.26.1.001
2. 2. Good congruences on abundant semigroups with $$PSQ$$ P S Q -adequate transversals vol.89, pp.2, 2014, doi:10.4134/CKMS.2011.26.1.001
3. 3. The product of quasi-ideal adequate transversals of an abundant semigroup vol.83, pp.2, 2011, doi:10.4134/CKMS.2011.26.1.001

#### 과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China, Natural Science Foundation of Shandong Province