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...

In this paper, we explore the relation between index of reducibility and Hilbert coefficients in local rings. Consequently, main result study provides a characterization sequentially Cohen-Macaulay ring terms its non-parameter ideals. As corollaries to theorem, obtain characterizations Gorenstein/Cohen-Macaulay Chern

Pinched Veronese rings are formed by removing an algebra generator from a subring of polynomial ring. We study the homological properties such rings, including Cohen-Macaulay, Gorenstein, and complete intersection properties. Greco Martino classified Cohen-Macaulayness pinched maximum entry exponent vector monomial; we re-prove their results with semigroup methods correct omission small class e...

We prove that sequentially Cohen-Macaulay rings in positive characteristic, as well as sequentially Cohen-Macaulay Stanley-Reisner rings in any characteristic, have trivial Lyubeznik table. Some other configurations of Lyubeznik tables are also provided depending on the deficiency modules of the ring.

We give several characterizations for the linearity property for a maximal Cohen-Macaulay module over a local or graded ring, as well as proofs of existence in some new cases. In particular, we prove that the existence of such modules is preserved when taking Segre products, as well as when passing to Veronese subrings in low dimensions. The former result even yields new results on the existenc...