Ideal category of a Noetherian ring

2023/04/07 by Romeo, P G, K, Minnumol P
#18Bxx #Category Theory (math.CT) #F.3.1 #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.03751

Abstract

In this paper we describe the categories \mathbbL_R , [ℝ_R] whose objects are left [right] ideals of a Noetherian ring R with unity and morphisms are appropriate R-linear transformations. Further it is shown that these are preadditive categories with zero object and are full subcategories of the R-modulue category with the property that these are categories with subobjects and the morphisms admits factorization property.

Related

• Ideal categories of rings and ring of cones
• Maximal ideals in module categories and applications
• Ideal Theory in Rings (Translation of "Idealtheorie in Ringbereichen" by Emmy Noether)
• Structure of modules stably annihilated by a fixed ideal
• The monomorphism category of Gorenstein projective modules and comparision with the category of matrix factorization