2

Part of 2019 Miklós Schweitzer

Problems(1)

Criterion for a ring to be simple

Source: Miklós Schweitzer 2019, Problem 2

R

be a noncommutative finite ring with multiplicative identity element

1

. Show that if the subring generated by

I \cup \{1\}

R

for each nonzero ideal

I

R

superior algebra