Equivalent Characterization of Localization Structure of Artin Rings and A Class of Quotient Rings
Let R be an Artin commutative ring,and mi(1≤i≤k)be the k maximal ideals of R.Through the Jacobson root nilpotent of Artin ring and chinese remainder theorem,it is obtained that the homomorphism from R to⊕R/mli is an isomorphism.Further,Artin rings are written as the direct sum of finite local rings Rei .It is found that each addition of direct sum is isomorphic to a quotient ring R/mli ,and it is isomorphic with local ring Rmi .
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