环及其本质理想

Rings and their Essential Ideals

小子模是与本质子模相对偶的概念,被广泛应用于小投射模的研究中.应用本质子模证明内射模是与小投射模相对偶的概念,并用本质理想来刻画几类的环:Noether环、hereditary环、V-环和半单环等.

Small submodules,as a notion dual to essential submodules,are widely applied to the study of small projective modules.In this paper,we prove that injective modules are dual to small projective modules by essential submodules.Moreover,some rings such as Noetherian rings,Hereditary rings,V-rings and semisimple rings,are characterized via essential ideals.