Abstract
In this paper, we show that a left artin ring A of global dimension at most two has Loewy length at most 2” - 1, where n is the number of simple components of A/rad(A). We assume that the reader is familiar with the trends (but not necessarily the details) of contemporary representation theory of artin rings. Let us record a few conventions. The rings discussed here will be left artinian, unless otherwise specified, and will sometimes be finite-dimensional algebras over an algebraically closed field, henceforth denoted by k. Modules will be finitely generated left modules unless otherwise specified. The radical of A will usually be denoted by r; the Loewy
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