Depth is a fundamental and important notations in algrbra. Meanwhile, depth found its importance in algebraic geometry, since it can help to study the properties of algebraic varieties. Hence, it is of great value to give characterization and generalization of depth. After a short recall of basic algebraic notations and properties, we succeed to generalize the notation of depth in the paper. What's more, we give some characterizations of the generalized depth and study its properties carefully. Let R be a N...
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