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In the present paper we investigate reflexive modules over the endomorphismalgebras of reflexive trace ideals in a one-dimensional Cohen-Macaulay localring. 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 itsmaximal ideal. We also explore the question of when the category of reflexivemodules is of finite type, i.e., the base ring has only finitely manyisomorphism classes of indecomposable reflexive modules. We show that, if thecategory is of finite type, the ring is analytically unramified and has onlyfinitely many Ulrich ideals. As a consequence, there are only finitely manyUlrich ideals are contained in Arf local rings once the normalization is alocal ring.

Reflexive modules over the endomorphism algebras of reflexive trace ideals