… The primary focus of this paper is the finiteness property of Ext-indices for certain ring
extensions. This is motivated by the following conjectures, all of which seem to be open. (See also […

… the vanishing of Ext-index of trivial extensions of Artinian rings. We put the new results into …
ring extensions of Artinian rings. Throughout, given a ring A, Ared will denote its reduced ring …

… property for some ring extensions. Note that any rings of the following types are known to be
AB rings. 1… 2) Cohen-Macaulay local rings with minimal multiplicity [3] [5]. 3) Gorenstein local …

… In particular, the counterexample of Heitmann [23] shows that one cannot expect such
rigidity results to hold in general local rings, so fiber product rings are indeed quite special. See …

… satisfying (AC), and in some cases we also obtain their converses, under the weaker
assumption that the ring has finite finitistic extension degree. The outline of this article is as follows. …

… of the finitistic extension degree of a Gorenstein ring, hence … under certain faithfully flat
ring extensions. Section 2 of this … base ring extensions R → R[x] when R is a Gorenstein ring, …

… As an example of this situation, let \(R \rightarrow S\) be a surjective ring homomorphism of
commutative noetherian rings. Then the Tate resolution of S over R is an extension of the DG …

… extensions of DG algebras under the above Ext vanishing assumptions, it is still an open
problem whether it holds along infinite free extensions of … certain endomorphism rings. Our first …

… the class of rings that do satisfy Auslander’s condition. We call them AC rings and show that
… The trivial extension of a commutative artinian local ring by its residue field; see [37, cor. 3.5]…

… The rings in [Citation12] are trivial extensions S ⋉ W , where S is a local ring and W is a
nonzero finitely generated semisimple S-module. Even when a local ring is not a trivial extension…