9 citations · 18 across the 13 of their papers we have counts for
16 papers
Modules of minimal multiplicity over one-dimensional Cohen-Macaulay local rings
Ela Celikbas, Olgur Celikbas, Naoki Endo +1
We study finitely generated modules of minimal multiplicity, a notion introduced by Puthenpurakal that extends the classical concept of minimal multiplicity from rings to modules.…
Full-Trace Modules
Ela Celikbas, Olgur Celikbas, Jürgen Herzog +1
Motivated by the definition of nearly Gorenstein rings, we introduce the notion of full-trace modules over commutative Noetherian local rings--namely, finitely generated modules wh…
On the vanishing of self extensions of even-periodic modules
Ela Celikbas, Olgur Celikbas, Hiroki Matsui +1
In this paper we study rigid modules over commutative Noetherian local rings, establish new freeness criteria for certain periodic rigid modules, and extend several results from th…
Traces of semi-invariants
Ela Celikbas, Jürgen Herzog, Shinya Kumashiro
This article investigates the traces of certain modules over rings of invariants associated with finite groups. More precisely, we provide a formula for computing the traces of arb…
On a generalization of Ulrich modules and its applications
Ela Celikbas, Olgur Celikbas, Justin Lyle +2
We study a modified version of the classical Ulrich modules, which we call -Ulrich. Unlike the traditional setting, -Ulrich modules always exist. We prove that these modules…
Classifying Betti Numbers of Fiber Products
Ela Celikbas, Hugh Geller, Tony Se
We consider fiber products of complete, local, noetherian algebras over a fixed residue field. Some of these rings cannot be minimally resolved with a free resolution using the rec…
Semidualizing Modules over Numerical Semigroup Rings
Ela Celikbas, Hugh Geller, Toshinori Kobayashi
A semidualizing module is a generalization of Grothendieck's dualizing module. For a local Cohen-Macaulay ring , the ring itself and its canonical module are always realized as…
Almost Gorenstein determinantal rings of symmetric matrices
Ela Celikbas, Naoki Endo, Jai Laxmi +1
We provide a characterization of the almost Gorenstein property of determinantal rings of a symmetric matrix of indeterminates over an infinite field. We give an explicit formula f…
Rees algebras of sparse determinantal ideals
Ela Celikbas, Emilie Dufresne, Louiza Fouli +4
We determine the defining equations of the Rees algebra and of the special fiber ring of the ideal of maximal minors of a sparse matrix. We prove that their initial alg…
On the ubiquity of Arf rings
Ela Celikbas, Olgur Celikbas, Cătălin Ciupercă +4
We introduce and develop the theory of weakly Arf rings, which is a generalization of Arf rings, initially defined by J. Lipman in 1971. We provide characterizations of weakly Arf…
Spinor structures on free resolutions of codimension four Gorenstein ideals
Ela Celikbas, Jai Laxmi, Jerzy Weyman
We analyze the structure of spinor coordinates on resolutions of Gorenstein ideals of codimension four. As an application we produce a family of such ideals with seven generators w…
The family of perfect ideals of codimension 3, of type 2 with 5 generators
Ela Celikbas, Jai Laxmi, Witold Kraśkiewicz +1
In this paper we define an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebr…
Generalized Gorenstein Arf rings
Ela Celikbas, Olgur Celikbas, Shiro Goto +1
In this paper we study generalized Gorenstein Arf rings; a class of one-dimensional Cohen-Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We o…
Associated Graded Rings and Connected Sums
H. Ananthnarayan, Ela Celikbas, Jai Laxmi +1
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate c…
Embeddings of canonical modules and resolutions of connected sums
Ela Celikbas, Jai Laxmi, Jerzy Weyman
For an ideal generated by all square-free monomials of degree in a polynomial ring with variables, we obtain a specific embedding of a canonical module of $R/…
Decomposing Gorenstein Rings as Connected Sums
H. Ananthnarayan, Ela Celikbas, Jai Laxmi +1
In 2012, Ananthnarayan, Avramov and Moore give a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. Given a Gorenstein ring, one woul…