中文摘要：

在关于交换环的高层正点定理和高层非负点定理的基础上,在交换环范畴中进一步建立了所谓的高层零点定理。同时,针对交换环上矩阵,获得了关于交换环上矩阵的高层正点定理,高层零点定理和高层非负点定理。该点定理可看作是关于交换环上矩阵的通常点定理的一种推广。

英文摘要：

Based on the Positivstellensatz and Nichtnegativstellensatz for higher level orderings in rings,a Nullstellensatz is further established for higher level orderings in rings.Moreover,it provides several higher level versions of Positivstellensatz,Nullstellensatz and Nichtnegativstellensatz for matrices over a commutative ring.The higher level Stellenstzen in this paper may be regarded as certain generalizations of the ordinary Stellenstzen for matrices over a commutative ring.