In this paper, we present an algorithmic method for computing a projective resolution of a module over an algebra over a field. If the algebra is finite dimensional, and the module is finitely generated, we have a computational way of obtaining a minimal projective resolution, maps included. This resolution turns out to be a graded resolution if our algebra and module are graded. We apply this ...

Syzygies capture intricate geometric properties of a subvariety in projective space. However, when the ambient space is a product of projective spaces or a more general smooth projective toric variety, minimal free resolutions over the Cox ring are too long and contain many geometrically superfluous summands. In this paper, we construct some much shorter free complexes that better encode the ge...

it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

We show that the infinite symmetric product of a connected graded-commutative algebra over ℚ is naturally isomorphic to free on positive degree subspace original algebra. In particular, commutative (in usual sense) graded polynomial Applied topology, we obtain quick proof Dold–Thom theorem in rational homotopy theory for spaces finite type. also products certain simple algebras are free; this a...

Following Johnsen and Verdure (2013), we can associate to any linear code $C$ an abstract simplicial complex in turn, a Stanley-Reisner ring $R_C$. The $R_C$ is standard graded algebra over field its projective dimension precisely the of $C$. Thus admits minimal free resolution resulting Betti numbers are known determine generalized Hamming weights question purity was considered by Ghorpade Sin...

In recent years, two different multigraded variants of Castelnuovo-Mumford regularity have been developed, namely multigraded regularity, defined by the vanishing of multigraded pieces of local cohomology modules, and the resolution regularity vector, defined by the multi-degrees in a minimal free resolution. In this paper, we study the relationship between multigraded regularity and the resolu...

We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph H appears within the resolution of its edge ideal I(H). We discuss when recursive formulas to compute the graded Betti numbers of I(H) in terms of its sub...

The Koszul homology of modules of the polynomial ring R is a central object in commutative algebra. It is strongly related with the minimal free resolution of these modules, and thus with regularity, Hilbert functions, etc. Here we consider the case of modules of the form R/I where I is a monomial ideal. So far, some good algorithms have been given in the literature and implemented in different...