近环中的基性和基性

Pub Date : 2021-01-01 DOI:10.4134/JKMS.J200013

G. Wendt

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引用次数: 0

摘要

在近环理论中存在几种不同类型的基元。这些都暗示了几种不同类型的素数。对于具有DCCN的近环，大多数类型的素数都暗示着某种类型的素数。我们可以证明，所谓的1素数近环也包含1素数。这使得我们可以用1素数的概念对具有链条件的近环上的极大理想进行分类，从而在近环结构理论中得到进一步的结果。

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PRIMENESS AND PRIMITIVITY IN NEAR-RINGS

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 nearrings 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.

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