Higher Level Stellens(?)tzen For Matrices Over A Commutative Ring

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