ε-算子和ε-Noether环.pdf

E一算子和g—Noether环基础数学专业研究生余琳指导教师王芳责(教授) 摘要本文主要研究了MFG整环上的￡,极大性***模,MFG整环,￡￡—Noether环的概念,即R是MFG整环且满足占一子模的升链条件,并对g—￡一有限型的可以判断R是￡￡一不可约子模,证明了￡一Noether模的任何真子模都有准素￡一子模的￡￡一Noether环上. 关键词:6一无挠模;极大性***理想;MFG整环;非极大素理想;}包络;￡一有限型模; ￡一Noether模:E—Noether环￡一Op erations and￡一N oetherRings Master:场Lin Pure Mathematics Supervisor:Wang Fanggui Abstrct This thesis mainly studies the￡一Operations on MFG ,we introduce G。torsionfree,max-injective modules,MFG domains,e-envelopes and deduce the ￡一Operations on MFG the basis define the E—modules offinite type and discuss therelated character we give the concept of￡一Noether rings which isdefined on MFG domains satisfying ACC on E-submodules,and give a seriesof characterizations on￡一Noether example,if every maximal idealoftheMFG domain R isof￡finite type,then R is aE—Noether introducing￡一irreducible submodules, we prove that any proper submodule of￡一Noether modules has￡ of primary￡,we extend the principal ideal theory on Noether rings to E-Noether rings. Keywords: 6一torsion free;max-injective ideals;MFG domains;non—maximal prime ideals;￡一envelopes;￡一modules offinitetype;￡一Noether modules;￡-Noether rings 目录箍要....................................··-······..一一一· ABSTRACT..................................···-··········· 1弓}言...........................................-.······· 2预备知识..............................................-.· ......................................... ***模.............................................. 3MFG整环土韵￡一算子.......................................... -"包终诱导的三一算子.......................................... ..............................................。. 4三一Noether环................................................ ......................................