48 papers
This paper introduces a local treatment of finite alignment for arbitrary higher-rank graphs by identifying a finitely aligned sub-constellation, which enables the construction of novel locally compact path and boundary-path groupoids that extend existing models and are proven to be amenable.
This paper introduces the concepts of strongly and weakly left Jacobson rings, establishes a one-sided noncommutative Nullstellensatz for polynomial rings over finite-dimensional algebras, and characterizes the Jacobson property for Azumaya algebras and algebras finitely generated over their centers.
This paper extends support variety theory from the compact to the non-compact part of a monoidal triangulated category in the noncommutative setting, establishing conditions under which the extended theory detects the zero object and thereby confirming a portion of a conjecture by the second author, Nakano, and Yakimov regarding central cohomological support in stable categories of finite tensor categories.
This paper documents research conducted under the DRP Turkiye 2025 mentorship program, providing a comprehensive exposition of Grassmann algebra's foundational properties, construction, and relationship to determinants, while culminating in a novel classification of its invariant subalgebras.
This paper investigates the fundamental structural properties and numerical prevalence of finite algebras within locally finite varieties of nonassociative linear algebras over finite fields, without assuming associativity or the Lie property.
This paper introduces a determinantal method for computing minimal local generalized additive decompositions (GADs) of homogeneous polynomials by minimizing the rank of symbolic inverse systems, proving that this approach guarantees finding all minimal decompositions without tensor extensions whenever the local GAD-rank does not exceed the form's degree.
This paper establishes a comprehensive theory of multiary graded polyadic algebras by extending classical group-graded algebras to higher-arity structures, introducing multiary group gradings, and uncovering unique phenomena such as higher power gradings and specific arity compatibility constraints through results like quantization rules and a First Isomorphism Theorem.
This paper introduces a unified Davis-Wielandt shell framework for the graphical stability analysis of MIMO LTI systems, proposing a novel rotated scaled relative graph (-SRG) concept that yields the least conservative closed-loop stability criterion among existing two-dimensional graphical conditions.
This paper surveys recent developments in the arithmetic of power monoids—structures formed by finite subsets of a monoid—and highlights their role in advancing factorization theory, particularly within non-cancellative and non-commutative settings.
This paper resolves the isomorphism problem for reduced finitary power monoids of cancellative monoids by proving that if one monoid is torsion, the power monoids are isomorphic if and only if the base monoids are, thereby confirming the result for torsion groups while leaving the general group case open.
This paper extends fractional linear transformations from Banach algebras to general rings via Wedderburn's continued fractions, establishing a connection to the projective elementary group PE(2,R) to define a length function and prove structural results regarding the perfectness and simplicity of its commutator subgroup.
This paper investigates homogeneous and inhomogeneous quaternionic Sylvester equations by establishing conditions for the existence of solutions and deriving their general and nonzero forms using quaternion square roots.
This paper introduces a systematic method for defining cochain complexes for dendriform and pre-Lie algebras by relating their cohomology to classical cohomology, thereby simplifying computations and leveraging established techniques.
This paper provides a complete classification of integrally closed domains and finitely generated torsion-free -algebras for which the ring of integer-valued polynomials is a Prüfer domain, proving that in the semiprimitive case, this property holds if and only if is a commutative finite direct product of almost Dedekind domains with finite residue fields satisfying specific boundedness conditions.
This paper investigates the arithmetic properties of factorizations in finitely-presented monoids by analyzing how presentation relations influence factorization behavior, constructing non-commutative fully elastic monoids, and proving that finitely-presented cancellative normalizing monoids satisfy the Structure Theorem for Unions.
This paper investigates equivalent characterizations of totally acyclicity for acyclic complexes of projective, injective, and flat modules over arbitrary rings, linking these conditions to homological invariants like silp(R), spli(R), and sfli(R) while refining existing results on the equality of these invariants and extending characterizations of Iwanaga-Gorenstein rings and the Nakayama conjecture to the non-commutative setting.
This paper investigates how various finitary conditions, such as weakly left noetherian and weakly left coherent properties, interact with graph products of monoids, establishing that these properties are preserved under retracts and proving that while the converse holds for most conditions, the weakly left noetherian property requires a precise characterization of the constituent monoids and their graph structure.
This paper proves that finite groups with semidihedral Sylow 2-subgroups possess a class-preserving Coleman outer automorphism group of odd order, thereby confirming that these groups satisfy the normalizer problem and extending existing results in the field.
This paper investigates the bifiltration of bracket ideals and the associated bivariate Hilbert polynomial for complex finite-dimensional filiform Lie algebras, demonstrating that this polynomial serves as a refined invariant capable of distinguishing isomorphism classes that remain indistinguishable by traditional numerical invariants related to centralizers and abelian ideal dimensions.
This paper establishes an explicit formula for the rank of the -walk matrix of the Dynkin graph and proves that its Smith normal form consists of a single 1, followed by twos, and the remaining entries being zero.