关键词: 半格, 逆半群, 分配格, 双半环, 偏序

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