47 citations · 47 across the 10 of their papers we have counts for
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A study of maximal shifts in the minimal graded free resolution of the residue field
Dinesh Limbu, Liana M. Şega, Adela Vraciu
We study two invariants, rate and slant, that describe the extremal behavior of the maximal shifts in the minimal free resolution of the residue field over a standard graded algebr…
Symbolic powers and integral closures via extremal ideals
Trung Chau, Art Duval, Sara Faridi +3
This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the…
Divisibility Relations and -Extremal ideals
Susan M. Cooper, Sabine El Khoury, Sara Faridi +3
A divisibility relation between the generators of a square-free monomial ideal formally encodes the situation when one generator divides the least common multiple of some other gen…
General symmetric ideals
Alexandra Seceleanu, Liana Şega
We investigate the structure and properties of symmetric ideals generated by general forms in the polynomial ring under the natural action of the symmetric group. This work signifi…
A study of a quadratic almost complete intersection ideal and its linked Gorenstein ideal
Rachel Diethorn, Sema Güntürkün, Alexis Hardesty +4
We examine the ideal in the polynomial ring , where is a field of characteristic zero or greater than . We…
Realizing resolutions of powers of extremal ideals
Trung Chau, Art M. Duval, Sara Faridi +3
Extremal ideals are a class of square-free monomial ideals which dominate and determine many algebraic invariants of powers of all square-free monomial ideals. For example, the $r^…
The mapping cone of an Eisenbud operator and applications to exact zero divisors
Liana M. Şega, Deepak Sireeshan
Let be a local ring that admits an exact pair of zero divisors , a -module with and a free resolution of over . We cons…
The minimal free resolution of a generic symmetric principal ideal
Megumi Harada, Alexandra Seceleanu, Liana Şega
We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of t…
DG module structures and minimal free resolutions modulo an exact zero-divisor
Liana M. Şega, Deepak Sireeshan
Let be a local ring with maximal ideal and let with . When is a finite -module with , we sho…
Detecting Koszulness and related homological properties from the algebra structure of Koszul homology
Amanda Croll, Roger Dellaca, Anjan Gupta +6
Let be a field and a standard graded -algebra. We denote by the homology algebra of the Koszul complex on a minimal set of generators of the irrelev…
Minimal quasi-complete intersection ideals
Andrew R. Kustin, Liana M. Şega, Adela Vraciu
A quasi-complete intersection (q.c.i.) ideal of a local ring is an ideal with "free exterior Koszul homology"; the definition can also be understood in terms of vanishing of André-…
On the linearity defect of the residue field
Liana Şega
Given a commutative Noetherian local ring , the linearity defect of a finitely generated -module , denoted $\ld_R(M)$, is an invariant that measures how far and its sy…
Free resolutions over short Gorenstein local rings
Inês B. Henriques, Liana M. Şega
Let R be a local ring with maximal ideal m admitting a non-zero element a\in\fm for which the ideal (0:a) is isomorphic to R/aR. We study minimal free resolutions of finitely gener…