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PRIMENESS AND PRIMITIVITY IN NEAR-RINGS
Gerhard Wendt 대한수학회 2021 대한수학회지 Vol.58 No.2
In near-ring theory several different types of primitivity exist. These all imply several different types of primeness. In case of near-rings with DCCN most of the types of primeness are known to imply primitivity of a certain kind. We are able to show that also so called $1$-prime near-rings imply $1$-primitivity. This enables us to classify maximal ideals in near-rings with chain condition with the concept of $1$-primeness which leads to further results in the structure theory of near-rings.