AI 中文总结
研究尼延胡伊斯代数的尼延胡伊斯模，引入相关概念并给出自由模构造，建立其与尼延胡伊斯算子环上模的关系，证明该模范畴有足够的投射、内射和平坦对象。
AI 中文摘要
本文研究尼延胡伊斯代数的尼延胡伊斯模。引入了自由、投射、内射和平坦尼延胡伊斯模的概念，并给出自由尼延胡伊斯模的构造。引入尼延胡伊斯算子环，通过证明相应范畴的同构建立尼延胡伊斯模与该环上模的关系。最后证明尼延胡伊斯模范畴有足够的投射、内射和平坦对象。
英文摘要
In this paper, we study the Nijenhuis modules of Nijenhuis algebras. The concepts of free, projective, injective, and flat Nijenhuis modules are introduced, and a construction of free Nijenhuis modules is given. The ring of Nijenhuis operators is introduced, and the relationship between Nijenhuis modules and modules over this ring is established by proving an isomorphism of the corresponding categories. Finally, it is proved that the category of Nijenhuis modules has enough projective, injective, and flat objects.
