56 papers
This paper provides proofs for Miyashita's characterizations of separable and Hirata separable polynomials in the general skew polynomial ring , extending the author's previous elementary proofs from the specific automorphism and derivation cases.
This paper presents a generating set for the initial ideal of simplicial toric ideals under the graded reverse lexicographic order by utilizing representations of affine monoid elements as sums of irreducibles, while also demonstrating how to derive the reduced Gröbner basis and comparing the maximal degree of the basis with the Castelnuovo-Mumford regularity.
This paper presents a unified combinatorial-algebraic framework for constructing multicyclic codes of arbitrary dimension over by utilizing -dimensional primitive idempotents and multidimensional cyclotomic orbits to establish a direct equivalence between algebraic and combinatorial descriptions, derive a natural polynomial basis, and generalize BCH and Reed-Solomon bounds through an efficient constructive algorithm.
This paper establishes a base change framework to extend tensor function results from specific fields to general fields, thereby proving that slice rank is linearly bounded by geometric rank and is quasi-supermultiplicative for any 3-tensors over any field.
This paper generalizes the classical multiplicity of an ideal to graded families of ideals on Noetherian local rings, establishing that many fundamental theorems (such as Rees' theorem and the Minkowski inequality) hold for this new invariant through simple proofs based on intersection products on blow-up schemes, independent of volume theory and Okounkov bodies.
This paper investigates the multigraded Betti numbers of Veronese embeddings by interpreting them through Hochster's formula as homology groups of specific simplicial complexes and utilizing Forman's discrete Morse theory to establish vanishing and non-vanishing results.
This paper explicitly constructs a generating set for the modular matrix invariant ring of the special linear group acting on $2 \times 2a2 \times 2$ matrices.
This paper characterizes the rings of invariants for finite orthogonal groups of plus type in odd characteristic and their corresponding Sylow subgroups in defining characteristic by constructing minimal generating sets, describing their relations, and proving that both rings are Cohen-Macaulay complete intersections.
This paper establishes relationships between the homological properties of the relative Frobenius morphism and the fibers of a map between commutative noetherian local rings containing a field of positive characteristic, with a specific focus on characterizing complete intersection and Gorenstein properties.
This paper characterizes multiplier ideals on normal schemes over via maps from pushforwards of dualizing sheaves under regular alterations, thereby providing a derived splinter characterization of klt singularities and an analogous description of test ideals in characteristic .
This paper establishes the equivalence of three notions of rank for matrices of multilinear forms, thereby generalizing Flanders' classical result, correcting prior work by Fortin and Reutenauer, resolving a question posed by Lampert, and proving a special case of the conjecture linking analytic and partition ranks of tensors.
This paper establishes a Galois connection framework for morphisms of neural codes using binary matrices to characterize boolean matrix factorization, define a partial order on codes based on free neurons, and introduce the concept of code defect to analyze covering relations in this poset.
This paper establishes that a Cohen-Macaulay complete local ring with an infinite residue field is uniformly dominant with explicit bounds on its dominant index under various conditions, including codimension 2 non-complete intersections, Burch rings, quasi-fiber product rings, and rings with low multiplicity, thereby recovering and refining existing results on hypersurfaces and specific ring classes.
This paper investigates the properties of tightly prime-divisor-finite domains (TPDF-domains), which are integral domains where every nonzero element has finitely many nonassociate prime divisors and every nonzero nonunit admits at least one prime divisor, while also examining how this property behaves under localization, constructions, and polynomial rings.
This paper introduces the concepts of vertex dismissible and scalable simplicial complexes as generalizations of vertex decomposability and shellability, establishing their algebraic characterizations via Alexander duality, proving their equivalence to weak connectedness for specific graph classes, and providing a unified skeletal framework that recovers numerous classical theorems.
This paper investigates partial trace ideals by establishing their properties, answering open questions posed by Maitra, deriving an upper bound for the invariant associated with the canonical module, and providing an explicit formula for this invariant in the specific case of numerical semigroup rings generated by three elements.
This paper investigates closed subschemes of dimension one in projective space defined by ideals with analytic spread at most , proving that under mild conditions their powers have positive depth, their Rees rings have regularity at most one, and their fiber cones are Cohen-Macaulay, results which notably apply to monomial curves in .
This paper establishes structural results for NIP integral domains, proving that non-field NIP Noetherian domains are semilocal of Krull dimension 1 with characteristic 0 fraction fields, that finite dp-rank domains are henselian local rings, and providing a classification of dp-minimal Noetherian domains.
This paper investigates a five-sequence of adjoint functors induced by functions between vertex sets of simplicial complexes, utilizing this structure to establish three categorical frameworks where the Stanley-Reisner correspondence yields dualities with commutative monomial rings.
This paper extends the theory of border bases from zero-dimensional to positive-dimensional homogeneous ideals by introducing the concept of homogeneous border bases relative to infinite order ideals and providing an effective criterion for their characterization using formal multiplication matrices that requires verification in only finitely many degrees.