MathDB
Problems
Contests
Undergraduate contests
Miklós Schweitzer
1960 Miklós Schweitzer
9
9
Part of
1960 Miklós Schweitzer
Problems
(1)
Miklós Schweitzer 1960- Problem 9
Source:
11/21/2015
9. Let
A
1
,
…
,
A
n
A_1, \dots , A_n
A
1
,
…
,
A
n
and
B
B
B
be ideals of an assoticative ring
R
R
R
such that
B
B
B
is contained in the set-union of the ideals
A
i
A_i
A
i
(
i
=
1
,
…
,
n
i=1, \dots , n
i
=
1
,
…
,
n
) but not contained in the union of any
n
−
1
n-1
n
−
1
of the ideals
A
i
A_i
A
i
. Show that, for some positive integer
k
k
k
,
B
k
B_k
B
k
is contained in the intersection of the ideals
A
i
A_i
A
i
. (A. 19)
college contests