广义Macaulay-Northcott模与包络

Generalized Macaulay-Northcott modules and envelopes

研究了广义Macaulay-Northcott模的包络性质。设M是右R-模,Ω是一个右R-模的类,E∈Ω,i:M→E是右R-模同态,证明了i:M→E是M的Ω-包络当且仅当[iS,≤]:[MS,≤]→[ES,≤]是[MS,≤]的[ΩS,≤]-包络,其中[MS,≤]是右R-模M上的广义Maucaulay-Northcott模;讨论了[MS,≤]的Galois群与M的Galois群之间的关系。

The envelope of generalized Macaulay-Norhtcott modules is discussed.Let M be a right R-module,Ω a class of right R-modules,E∈Ω and i：M→E a right R-homomorphism,it is shown that i：M→E is an Ω-envelope of M if and only if [iS,≤]：[MS,≤]→ [ES,≤] is an [ΩS,≤]-envelope of ,where is the generalized Maucaulay-Northcott module over the right R-module M.Also the relations between the Galois group of the module and the Galois group of the module M are described.