短正合列范畴C_RM

On Short Exact Categorie C_RM

通过讨论由短正合列及它们之间的态射构成的范畴CR M的相关性质[1～ 4 ] ,合理地定义了CR M中的同态核、象、正合列、复形、投射分解等概念 ,并由此得到环R的一种新维数 :正合 (左 )总体维数 .

We introduce a new category CRM which is a container for all short exact sequence of R-modules. Some basic propositions about this category have discussed. After the definitions of homomorphism, kernel of homomorphism, images, exact sequences, Chain complexes, project resolutions, etc, we get a new dimension associated with R, called exact (left) global dimension. Finally, we end the paper by the main result: the global dimension of ring R is equal to the exact global dimension of ring R.