Approach to Artinian Algebras via Natural Quivers
نویسندگان
چکیده
Given an Artinian algebra A over a field k, there are several combinatorial objects associated to A. They are the diagram DA as defined by Drozd and Kirichenko, the natural quiver ΔA defined by Li (cf. Section 2), and a generalized version of k-species (A/r, r/r2) with r being the Jacobson radical of A. When A is splitting over the field k, the diagram DA and the well-known Ext-quiver ΓA are the same. The main objective of this paper is to investigate the relations among these combinatorial objects and in turn to use these relations to give a characterization of the algebra A.
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