A result of Foxby, Reiten and Sharp says that a commutative noetherian local ring R admits
a dualizing module if and only if R is Cohen–Macaulay and a homomorphic image of a local …

We study the structure of the set of semidualizing complexes over a local ring. In particular,
we prove that for a pair of semidualizing complexes $ X_1 $ and $ X_2 $ such that $ G_ {X …

Let (R; m) be a local ring (commutative and Noetherian). If R is complete (or, more generally,
Henselian), one has the Krull-Schmidt uniqueness theorem for direct sums of …

Let (R, 𝔪, k) be a commutative Noetherian local ring. We study the suitable chains of
semidualizing R-modules. We prove that when R is Artinian, the existence of a suitable …

Let M be a finitely generated module over a commutative noetherian ring A (with 1). Then M
is called qtcusi-perfect if G-dim M= gradeM. Perfect modules (ie projective dimension …

We establish a characterization of dualizing modules among semidualizing modules. Let $
R $ be a finite dimensional commutative Noetherian ring with identity and $ C $ a …

Let R be a Cohen–Macaulay local ring of dimension one with a canonical module K R. Let I
be a faithful ideal of R. We explore the problem of when I⊗ RI∨ is torsionfree, where I∨ …

A finitely generated R-module C is semidualizing if the R-module homomorphism [special
characters omitted]: R→ Hom R (C, C) given by [special characters omitted](r)(c)= rc is an …

Let R be a ring, and let MR be a right R-module. Denote by V (M) the monoid of isomorphism
classed of direct summands of Mn for some n∈ N, and by V∗(M) the monoid of isomorphism …

Let (R, m) be a commutative noetherian local ring. Suppose that M and N are finitely
generated modules over R such that M has finite projective dimension and such that …