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In this article we have introduced and studied the notation of α-loewy modules (0-loewy modules is just a loewy module). Using this concept we extend some of the basic results of loewy modules to α-loewy modules and we find a universal upper bound for Krull dimension over ߙ- loewy rings. In particular, we show that module M has Krull dimension α if and only if each factor module of M is lambda-loewy modules for some lambda <=α and has finite Goldie dimension.