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 Primeness and primitivity in near-rings J. Korean Math. Soc. 2021 Vol. 58, No. 2, 309-326 https://doi.org/10.4134/JKMS.j200013Published online December 15, 2020Printed March 1, 2021 Gerhard Wendt Johannes Kepler Universit\"at Abstract : 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. Keywords : $1$-prime near-rings, $1$-primitive near-rings, maximal ideals, simple near-rings MSC numbers : 16Y30 Downloads: Full-text PDF   Full-text HTML