5 papers · 1 filter
Cellular resolutions of second powers of square-free monomial ideals with divisibility relations
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
Using divisibility relations between the generators of a square-free monomial ideal , we describe divisibility relations between the generators of the second power . We the…
Artinian Gorenstein algebras of embedding dimension four and socle degree three over an arbitrary field
Sabine El Khoury, Andrew R. Kustin
Let k be an arbitrary field, A be a standard graded Artinian Gorenstein k-algebra of embedding dimension four and socle degree three, and pi from P to A be a surjective graded homo…
The Scarf complex and betti numbers of powers of extremal ideals
Sabine El Khoury, Sara Faridi, Liana Sega +1
This paper is concerned with finding bounds on betti numbers and describing combinatorially and topologically (minimal) free resolutions of powers of ideals generated by a fixed nu…
Quadratically presented Gorenstein ideals
Sabine El Khoury, Andrew R. Kustin
Let be a quadratically presented grade three Gorenstein ideal in the standard graded polynomial ring , where is a field. Assume that satisfies the weak L…
Simplicial Resolutions of Powers of Square-free Monomial Ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +4
The Taylor resolution is almost never minimal for powers of monomial ideals, even in the square-free case. In this paper we introduce a smaller resolution for each power of any squ…