乘法半群为左正规纯正群的半环

Semirings for which multiplicative reducts are left normal orthogroups

研究了加法半群为半格,乘法半群为左正规纯正群的半环.证明了此类半环(S,+,·)可以嵌入到半格(S,+)的自同态半环中.构造S的一个特定的偏序关系,得到了(S,·)上的自然偏序与所构造偏序相等的等价条件.

In this paper, the semirings for which additive reducts are semilattices and multiplicative reducts are left normal orthogroups are studied. That semiring （S, ＋, .） is embedded into the endomorphism semiring of the semilattice （S, ＋） is proved. The partial order relation on semiring S is constructed and the equivalent condition in order to the natural order on multiplicative reduct of semiring S is equivalent to the constructed partial order on semiring S is obtained.