Abstract
LetR be a ring with non-zero identity and unitary leftR-modules, while\(\mathcal{N}_R \) is the subcategory of NoetherianR-modules. Given a length functionL on\(\mathcal{N}_R \) and central elements α1,...,α n ofR we can define the multiplicity length functione R (L|α1,...α n |) on\(\mathcal{N}_R \) with the same properties as the classical multiplicity. Here, we characterise multiplicity as the greatest length function which can be defined inductively in terms of a certain type of function on\(\mathcal{N}_R \).
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References
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Wright, D.J. A characterisation of multiplicity. Monatshefte fü Mathematik 79, 165–167 (1975). https://doi.org/10.1007/BF01585674
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DOI: https://doi.org/10.1007/BF01585674