A note on regular rings with stable range one.
Absolute stable rank and Witt cancellation for noncommutative rings.
Algebras whose Euler form is non-negative
An infinite torus braid yields a categorified Jones-Wenzl projector
A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which may serve as a categorification of the Jones-Wenzl projector.
Bases of minimal elements of some partially ordered free abelian groups
In the present paper, we will show that the set of minimal elements of a full affine semigroup contains a free basis of the group generated by in . This will be applied to the study of the group for a semilocal ring .
Categorifications of the polynomial ring
We develop a diagrammatic categorification of the polynomial ring ℤ[x]. Our categorification satisfies a version of Bernstein-Gelfand-Gelfand reciprocity property with the indecomposable projective modules corresponding to xⁿ and standard modules to (x-1)ⁿ in the Grothendieck ring.
Cohomological approaches to and of central simple algebras.
Computation of the mapping of factorization by the radical for of the endomorphism ring.
Corps gauches dont le groupe des commutateurs n'est pas égal au noyau de la norme réduite
D (...)+ and the Arting cokernel.
Decomposition of the Grothendieck group of stable categories of finite groups.
Diagonal reductions of matrices over exchange ideals
In this paper, we introduce related comparability for exchange ideals. Let be an exchange ideal of a ring . If satisfies related comparability, then for any regular matrix , there exist left invertible and right invertible such that for idempotents .
Exchange rings having stable range one.
Exchange rings in which all regular elements are one-sided unit-regular
Let be an exchange ring in which all regular elements are one-sided unit-regular. Then every regular element in is the sum of an idempotent and a one-sided unit. Furthermore, we extend this result to exchange rings satisfying related comparability.
Exchange rings satisfying the related comparability.
In this paper we investigate the related comparability over exchange rings. It is shown that an exchange ring R satisfies the related comparability if and only if for any regular x C R, there exists a related unit w C R and a group G in R such that wx C G.
Exchange rings with stable range one
We characterize exchange rings having stable range one. An exchange ring has stable range one if and only if for any regular , there exist an and a such that and if and only if for any regular , there exist and such that if and only if for any , .
Explicit Brauer induction.
Finitely Generated Projective modules over exchange rings.
Grothendieck and Witt Groups of Orders and Finite Groups.
Grothendieck group for the stable category of symmetric special biserial algebras.