Stable rank of corner rings
| dc.creator | Ara, P. | |
| dc.creator | Goodearl, K. R. | |
| dc.date | 2003-09-06 | |
| dc.date.accessioned | 2026-07-07T05:00:55Z | |
| dc.date.available | 2026-07-07T05:00:55Z | |
| dc.description | B. Blackadar recently proved that any full corner $pAp$ in a unital C*-algebra $A$ has K-theoretic stable rank greater than or equal to the stable rank of $A$. (Here $p$ is a projection in $A$, and fullness means that $ApA=A$.) This result is extended to arbitrary (unital) rings $A$ in the present paper: If $p$ is a full idempotent in $A$, then $sr(pAp) \geq sr(A)$. The proofs rely partly on algebraic analogs of Blackadar's methods, and partly on a new technique for reducing problems of higher stable rank to a concept of stable rank one for skew (rectangular) corners $pAq$. The main result yields estimates relating stable ranks of Morita equivalent rings. In particular, if $B$ is isomorphic to the endomorphism ring of a finitely generated projective generator $P_A$ which can be generated by $n$ elements, then $sr(A) \leq n{\cdot}sr(B)-n+1$. | |
| dc.identifier | https://arxiv.org/abs/math/0309116 | |
| dc.identifier | http://arxiv.org/abs/math/0309116 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68495 | |
| dc.subject | Rings and Algebras | |
| dc.subject | K-Theory and Homology | |
| dc.subject | 19B10; 16S50 | |
| dc.title | Stable rank of corner rings | |
| dc.type | text |