This paper determines when the Krull-Schmidt property holds for all finitely generated modules and for maximal Cohen-Macaulay modules over one-dimensional local rings with finite Cohen-Macaulay type. We classify all maximal CohenMacaulay modules over these rings, beginning with the complete rings where the Krull-Schmidt property is known to hold. We are then able to determine when the Krull-Sch...

R.G. and Perez proved that under certain conditions the test ideal of a module closure agrees with trace closure. We use this fact to compute ideals various rings respect closures coming from their indecomposable maximal Cohen–Macaulay modules. also give an easier way hypersurface ring in three variables particular type matrix factorization.

We provide a generalization of pseudo-Frobenius numbers numerical semigroups to the context simplicial affine semigroups. In this way, we characterize Cohen-Macaulay type semigroup ring K[S]. define S, type(S), in terms some Apéry sets S and show that it coincides with ring, when K[S] is Cohen-Macaulay. If d-dimensional embedding dimension at most d+2, then type(S)?2. Otherwise, type(S) might b...

s. 1 Let (R,m) be a Noetherian local ring which is a quotient of a Gorenstein local ring. Let M be a finitely generated R-module. In this paper, we study the structure of the canonical module K(RnM) of the idealization RnM via the polynomial type introduced by N. T. Cuong [5]. In particular, we give a characterization for K(RnM) being Cohen-Macaulay and generalized Cohen-Macaulay.