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PRIMENESS AND PRIMITIVITY IN NEAR-RINGS

  • Wendt, Gerhard (Department of Algebra Johannes Kepler Universitat)
  • Received : 2020.01.09
  • Accepted : 2020.07.21
  • Published : 2021.03.01

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.