2023/01/25 by Naoki Endo, Endo, Naoki, Shirô Gotô +1 · 1 citation
Mathematics · Medicine · #13A15 #13C14 #13H10 #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Intracranial Aneurysms: Treatment and Complications
paper · pdf · doi:10.48550/arxiv.2301.10401
openalex publication_date 2023/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the present paper we investigate reflexive modules over the endomorphism algebras of reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem generalizes both of the results of S. Goto, N. Matsuoka, and T. T. Phuong and T. Kobayashi concerning the endomorphism algebra of its maximal ideal. We also explore the question of when the category of reflexive modules is of finite type, i.e., the base ring has only finitely many isomorphism classes of indecomposable reflexive modules. We show that, if the category is of finite type, the ring is analytically unramified and has only finitely many Ulrich ideals. As a consequence, there are only finitely many Ulrich ideals are contained in Arf local rings once the normalization is a local ring.