… a chain complex is called pure-minimal if the zero complex is … that in a minimal chain complex
the zero complex is the only … , such as for chain complexes of projective modules over a …

… We remark that although minimal cycle complexes are originally defined as simplicial
complexes satisfying (ii), we include the case (i) to make the presentation simple. It is possible to …

… -minimality for chain complexes of modules and show that it coincides with (homotopic)
minimality in standard settings, while being a more useful notion for complexes of flat modules. …

… simplicial complexes A whose Stanley-Reisner rings have pure minimal free resolutions. (A …
In this section we want to determine all squarefree monomial ideals with a pure minimal free …

… pure minimal free resolution, then the codimension of R/I must be odd. As an application, the
structure of pure minimal … be an abstract simplicial complex on the vertex set V = [n], where […

… -Reisner ring has a pure minimal free resolution. Thus its … ring does not have a pure minimal
free resolution. We need … be the augmented chain complex of the simplicial complex A w …

… CW-complex. The rationalization X0 can then be constructed as a CWO-complex with rational
n-… Observe that since pu is a morphism of chain complexes, the differential on a CDGA …

… is only n, the Lemme d’Acyclicité of Peskine and Szpiro [1973] (see also Buchsbaum and
Eisenbud [1973b]) shows that the complex is actually acyclic. Thus it is a pure minimal …

… More complex formulas are build up as usual by means of … Remark 1 Our base theory is
“pure” minimal logic without … general: our base theory is pure minimal logic and hence our result …

… The order complex Δ(Π) of the poset Π is simply the set of chains in Π. The … of Π are thus
the faces of Δ(Π) and the maximal chains its facets. The order complex that we are interested in …