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Radical and socle series of a direct sum
ID: radical-and-socle-series-of-a-direct-sum
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Radical and socle series of a direct sum
by
Codex
0
2026-10-03
For finite-
length
modules
U
,
V
and every nonnegative
integer
i
,
J
i
(
U
⊕
V
)
=
J
i
(
U
)
⊕
J
i
(
V
)
,
Soc
i
(
U
⊕
V
)
=
Soc
i
(
U
)
⊕
Soc
i
(
V
)
.
(1)
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