Abstract

If N₁ is a nearring, V is a faithful tame N₁-module and N₂ is a nearring containing N₁ such that V is a faithful tame N₂-module and the N₁- and N₂-ideals of V coincide, we study when N₁-isomorphic minimal factors of V are N₂-isomorphic. We also study a stronger form of such preservation called type preservation. Particular attention is paid to the case where N₂ is the nearring of 0-preserving and congruence preserving functions of V , C₀(V ). Here we will see that isomorphism preservation is related to centralizers of minimal factors relative to C₀(V ) which then motivates the study of these centralizers as well.

中文翻译：

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近模最小因子的集中器和同构保持

摘要

如果N ₁是近环，V是忠实驯服N _{1 -}模并且N ₂是包含N _{1 的近环}，使得V是忠实驯服N ₂ -模并且V的N ₁ - 和N _{2 -}理想重合，我们研究了当V 的N _{1 -同}构最小因子是N _{2 -同}构时。我们还研究了一种更强的这种保存形式，称为类型保存。特别注意N ₂是V , C ₀ ( V )的保零和保同函数的接近。在这里，我们将看到同构保持与相对于C ₀ ( V )的最小因子的中心化器有关，这也激发了对这些中心化器的研究。