Semirings whose multiplicative reduct is inverse semigroup
Pan Xiu-juan · Journal of Northwest University · 2006
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.