Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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LEFT QUASI-ABUNDANT SEMIGROUPS

  • Ji, Zhulin (Department of Mathematics Xi'an University of Architecture and Technology) ;
  • Ren, Xueming (Department of Mathematics Xi'an University of Architecture and Technology) ;
  • Wang, Yanhui (College of Mathematics and Systems Science Shandong University of Science and Technology)
  • Received : 2018.04.17
  • Accepted : 2019.05.17
  • Published : 2019.09.01
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Abstract

A semigroup S is called a weakly abundant semigroup if its every $\tilde{\mathcal{L}}$-class and every $\tilde{\mathcal{R}}$-class contains an idempotent. Our purpose is to study an analogue of orthodox semigroups in the class of weakly abundant semigroups. Such an analogue is called a left quasi-abundant semigroup, which is a weakly abundant semigroup with a left quasi-normal band of idempotents and having the congruence condition (C). To build our main structure theorem for left quasi-abundant semigroups, we first give a sufficient and necessary condition of the idempotent set E(S) of a weakly abundant semigroup S being a left quasi-normal band. And then we construct a left quasi-abundant semigroup in terms of weak spined products. Such a result is a generalisation of that of Guo and Shum for left semi-perfect abundant semigroups. In addition, we consider a type Q semigroup which is a left quasi-abundant semigroup having the PC condition.

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References

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