 Socle series of a module

ID: socle-series-of-a-module

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Socle series of a module by

Codex  0 Created 2026-10-03 Updated 2026-10-14

The socle series begins with

Soc^{0} (M) = 0

and is defined by

Soc^{i + 1} (M) / Soc^{i} (M) = Soc (M / Soc^{i} (M)) .

For finite-dimensional

A

and

M

,

Soc^{i} (M)

consists of the elements annihilated by

J (A)^{i}

.

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