The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
Derivations of two-step nilp otent alge- bras
10 Pith papers cite this work. Polarity classification is still indexing.
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Proves Kazhdan isomorphism between Hecke algebras of n-fold metaplectic SL2 covers over sufficiently close local fields F and F' with residue char coprime to n and containing nth roots of unity.
Introduces the three-cosystole invariant for matroids and proves its optimal upper bound among regular matroids of rank at most six via monotonicity under extensions and explicit estimates on maximal simple examples.
Non-nilpotent Leibniz algebras with 1-dimensional derived subalgebra over fields of char ≠2 are isomorphic to the direct sum of a 2-dimensional non-Lie Leibniz algebra and an abelian algebra.
Proves sup pd(Flat_R) = sup Gpd(GFlat_R) for arbitrary rings, giving Gorenstein-based characterizations of n-perfect and weakly n-Σ-cotorsion rings.
Cochordal zero-divisor graphs of chain rings admit refined Betti formulas yielding 2-linear resolutions for the studied quotient rings.
Factorization theorems with sharp bounds and an extension of the Dumas irreducibility criterion to formal power series over PIDs and DVRs using Newton polygons and constant term factorizations.
Upper bounds on the number of irreducible factors of certain integer polynomials are obtained from prime factorizations of evaluated values and complex root locations, extending to bivariate polynomials via non-Archimedean valuations.
Generalizes Iarrobino's symmetric decomposition to self-dual modules over local algebras, classifies local Hilbert functions for small degrees, and extends Kunte's self-duality criterion.
Incidence toric ideals for t-subsets in k-subsets are interpreted with generators as null t-designs and balanced orientable normal d-pseudomanifolds, with octahedra generators playing a key structural role.
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Non-nilpotent Leibniz algebras with one-dimensional derived subalgebra
Non-nilpotent Leibniz algebras with 1-dimensional derived subalgebra over fields of char ≠2 are isomorphic to the direct sum of a 2-dimensional non-Lie Leibniz algebra and an abelian algebra.
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On classical and Gorenstein homological invariants of rings
Proves sup pd(Flat_R) = sup Gpd(GFlat_R) for arbitrary rings, giving Gorenstein-based characterizations of n-perfect and weakly n-Σ-cotorsion rings.