半环簇$CO{S}_n^{+}$的一些子簇

Some Subvarieties of Semiring Variety $CO{S}_n^{+}$

摘要: 研究半环簇$CO{S}_n^{+}$ 中半环的格林关系，给出此类半环的$\stackrel{+}{H}\wedge \stackrel{\cdot }{L},\stackrel{+}{H}\wedge \stackrel{\cdot }{R},\stackrel{+}{H}\wedge \stackrel{\cdot }{D},\stackrel{+}{H}\vee \stackrel{\cdot }{L},\stackrel{+}{H}\vee \stackrel{\cdot }{R},\stackrel{+}{H}\vee \stackrel{\cdot }{D}$ 关系的等价刻画，得到上述关系为同余的充分必要条件，证明由上述格林关系决定的半环类都是$CO{S}_n^{+}$ 的子簇。

Abstract: This paper mainly studies the Green’s relations of $CO{S}_n^{+}$ , discusses the characterizations of the Green’s relations of $\stackrel{+}{H}\wedge \stackrel{\cdot }{L},\stackrel{+}{H}\wedge \stackrel{\cdot }{R},\stackrel{+}{H}\wedge \stackrel{\cdot }{D},\stackrel{+}{H}\vee \stackrel{\cdot }{L},\stackrel{+}{H}\vee \stackrel{\cdot }{R},\stackrel{+}{H}\vee \stackrel{\cdot }{D}$ and obtains the necessary and sufficient conditions for the above relations to be congruent. It is proved that the semiring classes determined by these relations are all subvarieties of $CO{S}_n^{+}$ .