偏序半群的商序同态研究

Study on Quotient Ordered Homomorphisms of Partially Ordered Semigroups

通过偏序半群的商半拟序、商半拟链和正则同余,研究了偏序半群的商序同态,给出了偏序半群的商序同态基本定理。同时,讨论了偏序半群的商半拟序与商序同态之间的关系,给出了由偏序半群S到T的商序同态φ构造S的商半拟序ρ_φ的方法以及S的一个商半拟序ρ?ρ_φ的充分必要条件,并得到了一些重要结论。

By quotient semi-pseudo order,quotient semi-pseudo chain and regular congruence of partially ordered semigroups,the quotient ordered homomorphisms of partially ordered semigroups are studied,and the fundamental theorems on quotient ordered homomorphisms are given.At the same time,relationships between quotient semi-pseudoorder and quotient ordered homomorphisms of par-tially ordered semigroups are discussed,the construction method on quotient semi-pseudo order of S by quotient ordered homomorphisms from partially ordered semigroups S to T and the sufficient and the necessary conditions on a quotient semi-pseudo orderρ⊆ρφof S are given,and some important conclu-sions are obtained.