A nonempty set R is said to be a ring if we can dene two binary operationsin R, denoted by + and respectively, such that for all a; b; c 2 R, R is an Abelian groupunder addition, closed under multiplication, and satisfy the associative law under multi-plication and distributive law. Let R be a ring. R is an Artin ring if every nonempty setof ideals has the minimal element. In this paper, the Artin ring and some characteristicsof it will be discussed.
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