… coherent … X-coherent rings. We then investigate the relations among Gorenstein nX-injective,
nX-flat, injective and flat modules on X-FC-rings (ie, self nX-injective and nXcoherent rings). …

… In recent years, the Gorenstein homological theory for graded rings has become an … [34]
the homological behavior of the FP-gr-injective modules on gr-coherent rings was investigated. …

… extensions of M, iterated extensions of M and the compactly supported perverse coherent …
that the homology H•(Mf,ζ (Y,M), φW f ) of the space of ζ-stable, f-framed perverse coherent …

… homology may be obtained as a colimit uni-dimensional … Secondly, we link persistent
homology to natural homology, … natural homology, an untractable invariant, from uni-dimensional …

… , such as relative homological dimensions, left and … homological dimensions that comes
from the class GF(F,A). In Section 4 we study the natural finitistic and weak global dimensions …

… derived category D(R) of a ring R of weak global dimension at most one we consider t-…
coaisles do not always arise from homological ring epimorphisms. We also consider a non-…

… sheaves in algebraic geometry, and then developed, under the influence of Noetherian
ring theory and homology, towards a full-fledged topic in algebra. During the past 30 years, …

… In Table 4, we have summarized the computations of cohomology rings which we have
formalized. The additions to the library required for these computation amount to about 8800 …

… Furthermore, if R is a commutative n-perfect ring, we prove that $$\mathrm {fPD}(R)<+\infty
$$ fPD ( R ) < + ∞ if and only if $$\mathrm {sup}_{{\mathfrak {m}}\in \mathrm {Max}R}\mathrm {…

… -invariant trace from the factorization homology of the circle $ {… is a calculation of the
factorization homology over the circle of … Poincar\'e duality for 1-dimensional factorization …