摘要
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.
出处
《西北大学学报(自然科学版)》
CAS
CSCD
北大核心
2006年第3期345-347,共3页
Journal of Northwest University(Natural Science Edition)
基金
陕西省自然科学研究基金资助项目(2003A10)
陕西省教育厅自然科学专项基金资助项目(02JK053)
关键词
半群
半环
半格
分配格
偏序关系
semigroups
semirings
semilattices
distributive lattices
partial ordered relations