56 papers
This paper investigates how algebraic invariants of edge ideals change under selective graph suspensions, demonstrating that while suspensions over minimal vertex covers consistently preserve regularity and increase projective dimension by one, suspensions over maximal independent sets exhibit uniform behavior only for paths and cycles, with a specific extremal family of paths showing increases in both regularity and the -invariant.
This paper investigates the set of lattice points formed by pairs of Castelnuovo-Mumford regularity and v-number for edge ideals of connected graphs, establishing general bounds and explicitly characterizing these pairs for whisker and Cameron-Walker graphs while proposing a conjecture for connected chordal graphs.
This paper establishes a characterization of the small finitistic dimension of a commutative ring in terms of the vanishing of Ext groups for finitely generated ideals, proving that fPD if and only if the vanishing of for implies its vanishing for all , and applies this result to derive the inequality fPD and analyze various classes of rings such as -rings and DW-rings.
This paper presents an efficient algorithm that utilizes partial Gröbner basis computation and sparse interpolation to find simple generating sets for subfields of rational function fields, demonstrating improved performance and practical utility in applications like structural parameter identifiability.
This paper establishes a generic flatness result for the cohomology of thickenings of smooth projective schemes over characteristic zero Noetherian domains, while simultaneously demonstrating that for nine points in the projective plane, the associated local cohomology module fails to be generically free and possesses infinitely many associated prime ideals, thereby addressing open questions regarding the constancy of the least degree of hypersurfaces with prescribed multiplicities.
This paper introduces the concept of uniformly dominant local rings, establishes sufficient conditions for their existence in various classes such as Burch rings, and derives upper bounds for the Orlov spectrum of their singularity categories while demonstrating the preservation of this property under basic operations.
This paper presents a formalization in Lean of the foundational commutative algebra result that projectivity of an -module descends along a faithfully flat ring map, thereby verifying Perry's correction to a subtle gap in the classical work of Raynaud and Gruson.
This paper presents a randomized polynomial-time algorithm for learning read-once determinants by establishing its equivalence to a black-box version of the Principal Minor Assignment Problem and resolving the latter through the introduction of the rank-one extension property.
This thesis extends the relative -contractibility of Koras-Russell threefolds and their higher-dimensional prototypes to arbitrary Noetherian base schemes, thereby establishing the existence of the first known family of smooth "exotic" motivic spheres in dimensions that are -homotopic to, but not isomorphic to, the punctured affine space .
This paper establishes that modules over specific classes of Gorenstein local rings, including those where is a Golod ring or the square of the maximal ideal is generated by at most two elements, possess rational Poincaré series with a common denominator, thereby confirming the Auslander-Reiten conjecture for these rings and providing new proofs for existing results on compressed and low codepth rings.
This paper introduces a class of algebras derived from labeled directed graphs, establishes their properties as axial algebras with specific fusion laws and simplicity, and demonstrates that any group can be realized as the automorphism group of infinitely many such simple algebras.
This paper presents a construction for linear quotient orderings of products of two ideals with linear quotients and applies it to demonstrate that the squares and cubes of a specific class of modified anticycle graphs also possess linear quotients.
This paper investigates the natural action of the Galois group on the class group of a Galois number field through a direct approach, utilizing the class groups of overrings and the arithmetic of normsets to elucidate the relationship between these algebraic structures.
This paper establishes that for monomial ideals in polynomial rings with two or three variables, the Castelnuovo–Mumford regularity of the integral closure is bounded by that of the ideal itself, and characterizes ideals generated in a single degree as having regularity equal to that degree if and only if they possess linear quotients.
This paper clarifies the ring-theoretic and homological properties of the tilt of extensions between perfectoid rings, building upon Faltings' almost étale extensions and Scholze's tilting operations to advance the construction of big Cohen-Macaulay algebras.
This paper investigates the division properties of commuting polynomials with rational and integer coefficients, revealing algebraic particularities related to weighted sums on cycle graphs with pendant edges and exploring commuting polynomials over fields of positive characteristic.