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Radical and socle series of a direct sum
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Mathematics
Area of mathematics
Algebra
Commutative algebra
Module theory
Loewy length
2026-10-03
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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)
Ancestors
(7)
Loewy length
Module theory
Commutative algebra
Algebra
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2019
/
iii
/
Paper 138
/
1
/
b
/
Solution
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