SHANDONG SCIENCE ›› 2018, Vol. 31 ›› Issue (2): 100-104.doi: 10.3976/j.issn.1002-4026.2018.02.016

• Other Research Article • Previous Articles     Next Articles

Bi-semiring whose multiplicative semigroup(S,·)is an inverse semigroup

YUAN Meng, LI Gang*   

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
  • Received:2017-04-20 Published:2018-04-20 Online:2018-04-20

Abstract:

A bi-semiring whose semigroup S,+ was a semilattice, semigroup  S,· was an inverse semigroup and semiroup S,* was a semilattice was studied in this paper. By using three partial orders constructed on S,+,S,· and S,* and the relationships among them, some equivalent statements for this kind of bisemiring to be a distributive lattice were given.

Key words: inverse semigroup, distributive lattice, semilattice, partial order, bi-semiring

CLC Number: 

  • O152. 7

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