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Loewy length
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Algebra
Commutative algebra
Module theory
2026-10-03
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The Loewy
length
of
a
finite-
length
module
is both the least
m
for which
J
m
(
M
)
=
0
and the least
m
for which
Soc
m
(
M
)
=
M
.
Table of contents
Radical and socle series of a direct sum
Loewy length
Radical and socle series of a direct sum
0
0
0
Loewy length
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
(6)
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
/
d
/
ii
/
Solution
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