The nilpotency of near-rings
The nilpotency of torsion-free rings with given type set
The N*-Metric Completion of Regular Rings.
The normal elements of an algebra of general matrices are central.
The number of complete exceptional sequences for a Dynkin algebra
The Dynkin algebras are the hereditary artin algebras of finite representation type. The paper determines the number of complete exceptional sequences for any Dynkin algebra. Since the complete exceptional sequences for a Dynkin algebra of Dynkin type Δ correspond bijectively to the maximal chains in the lattice of non-crossing partitions of type Δ, the calculations presented here may also be considered as a categorification of the corresponding result for non-crossing partitions.
The number of elements in the mutation class of a quiver of type .
The number of indecomposable Schur rings over a cyclic 2-group.
The order of algebras with nontrivial fixed point subalgebras.
The p. p. ring and the Pierce sheaf representation of non-commutative rings
The parametrization of interior algebras.
The periodicity conjecture for blocks of group algebras
We describe the representation-infinite blocks B of the group algebras KG of finite groups G over algebraically closed fields K for which all simple modules are periodic with respect to the action of the syzygy operators. In particular, we prove that all such blocks B are periodic algebras of period 4. This confirms the periodicity conjecture for blocks of group algebras.
The Picard group of the Burnside ring.
The Prime Ideal Theorem in Non-Commutative Arithmetic.
The Prime Spectrum of the Enveloping Algebra of a Reductive Lie Algebra.
The primitivity of semigroup algebras of free products.
The product of trees in the Loday-Ronco algebra through Catalan alternative tableaux.
The pro-unipotent radical of the pro-algebraic fundamental group of a compact Kähler manifold
The aim of this paper is to study the pro-algebraic fundamental group of a compact Kähler manifold. Following work by Simpson, the structure of this group’s pro-reductive quotient is already well understood. We show that Hodge-theoretic methods can also be used to establish that the pro-unipotent radical is quadratically presented. This generalises both Deligne et al.’s result on the de Rham fundamental group, and Goldman and Millson’s result on deforming representations of Kähler groups, and can...
The pure-projective ideal of a module category
The quasi-hereditary algebra associated to the radical bimodule over a hereditary algebra
Let Γ be a finite-dimensional hereditary basic algebra. We consider the radical rad Γ as a Γ-bimodule. It is known that there exists a quasi-hereditary algebra 𝓐 such that the category of matrices over rad Γ is equivalent to the category of Δ-filtered 𝓐-modules ℱ(𝓐,Δ). In this note we determine the quasi-hereditary algebra 𝓐 and prove certain properties of its module category.
The radicalness of polynomial rings over nil rings.