… Gorenstein local finite-dimensional algebras, ie local finite-dimensional algebras A with the
maximal ideal \({\mathfrak … \in A\mid a \mathfrak {m}= 0\}\) is one-dimensional. They show that …

… \(I/I^2\) has finite projective dimension over R/I, then I must be … Kähler differentials has finite
projective dimension; we prove … {\mathfrak {m}}_{R/I}\) factors through a finitely generated R/I-…

… If we suppose that \(\mathfrak {m}\) is finitely generated, we call the embedding dimension
of A … We denote the Koszul complex related to x by \(\mathbb {K}_{\bullet }(\mathbf {x})\). The …

… R-module with the finite projective dimension p. Also, let N be … is a local ring and c is equal
to the dimension of N, we give a … Also, if M is finitely generated with finite projective dimension …

… -dimension can be used to give a homological characterization of Gorenstein rings, similar to
the way projective dimension … with \(\mathfrak {m}^2=0\) are either Gorenstein or G-regular. …

… is Gorenstein if the classes of #A-modules of finite projective and finite injective dimensions
… by modules M such that #M is of finite projective and injective dimensions as an #A-module. …

… of \({\mathfrak {g}}\) into the integer homology lattice of X. We then … of X becomes fully physical
in the M-theory picture; its size … (we will explain the term ‘Gorenstein’ and how to diagnose …

… We develop theory of (possibly large) cotilting objects of injective dimension at most one
in general Grothendieck categories. We show that such cotilting objects are always pure-…

… 0-dimensional rings… X) is a Q-Noetherian ring and let \({\mathfrak {p}}\) be a prime ideal of
R. By Lemma 1.12, we have that \({\mathfrak {p}}R(X)\) is a prime ideal of R(X), and hence \(R(X…

… identifying a triangulated catgory to be Gorenstein and an artin algebra to be F-Gorenstein. …
The ξ-projective dimension ξ-pdA of A ∈ C is defined inductively. If A ∈ P(ξ), then define ξ-…