乘法半群(S,·)是逆半群的双半环

摘要

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.%本文研究了(S,+)半群为半格、(S,·)半群为逆半群、(S,*)半群为半格的双半环,利用加法半群(S,+)、乘法半群(S,·)和乘法半群(S,*)上的偏序以及三者之间的关系,给出了该类双半环成为分配格的几个等价命题.