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Romanian National Olympiad 2018 - Grade 12 - problem 1
Romanian National Olympiad 2018 - Grade 12 - problem 1
Source: Romania NMO - 2018
April 7, 2018
superior algebra
Ring Theory
Problem Statement
Let
A
A
A
be a finite ring and
a
,
b
∈
A
,
a,b \in A,
a
,
b
∈
A
,
such that
(
a
b
−
1
)
b
=
0.
(ab-1)b=0.
(
ab
−
1
)
b
=
0.
Prove that
b
(
a
b
−
1
)
=
0.
b(ab-1)=0.
b
(
ab
−
1
)
=
0.
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