乘法半群为逆半群的半环

Semirings whose multiplicative reduct is inverse semigroup

目的求证加法导出是半格、乘法导出是逆半群的半环成为分配格的充要条件。方法加法半群和乘法半群上的偏序以及二者之间的关系。结果给出了该类半环成为分配格的几个等价命题。结论推广了双半格成为分配格的一些结果。

Aim In order to prove a semiring whose additive reduct is a semilattice and multiplicative reduct is a inverse semigroup to be a distributive lattice. Methods Using partial orders on multiplicative reduct and additive reduct and relations between two partial orders. Results Some equivalent statements are obtained concerning a semiring becoming a distributive lattice. Conclusion Some known results about bi-semilattice becoming distributive lattice are expanded.