Extensions and pullbacks in QB-rings

Pere Ara; Gert K. Pedersen; Francesc Perera

doi:https://doi.org/10.1007/s10468-004-5767-x

Extensions and pullbacks in QB-rings

Pere Ara, Gert K. Pedersen, Francesc Perera

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

We prove a new extension result for QB-rings that allows us to examine extensions of rings where the ideal is purely infinite and simple. We then use this result to explore various constructions that provide new examples of QB-rings. More concretely, we show that a surjective pullback of two QB-rings is usually again a QB-ring. Specializing to the case of an extension of a semi-prime ideal I of a unital ring R, the pullback setting leads naturally to the study of rings whose multiplier rings are QB-rings. For a wide class of regular rings, we give necessary and sufficient conditions for their multiplier rings to be QB-rings. Our analysis is based on the study of extensions and the use of nonstable K-theoretical techniques. © Springer 2005.

Original language	English
Pages (from-to)	75-97
Journal	Algebras and Representation Theory
Volume	8
DOIs	https://doi.org/10.1007/s10468-004-5767-x
Publication status	Published - 1 Mar 2005

Keywords

Exchange ring
Multiplier ring
Purely infinite simple ring
QB-ring

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T1 - Extensions and pullbacks in QB-rings

AU - Ara, Pere

AU - Pedersen, Gert K.

AU - Perera, Francesc

PY - 2005/3/1

Y1 - 2005/3/1

N2 - We prove a new extension result for QB-rings that allows us to examine extensions of rings where the ideal is purely infinite and simple. We then use this result to explore various constructions that provide new examples of QB-rings. More concretely, we show that a surjective pullback of two QB-rings is usually again a QB-ring. Specializing to the case of an extension of a semi-prime ideal I of a unital ring R, the pullback setting leads naturally to the study of rings whose multiplier rings are QB-rings. For a wide class of regular rings, we give necessary and sufficient conditions for their multiplier rings to be QB-rings. Our analysis is based on the study of extensions and the use of nonstable K-theoretical techniques. © Springer 2005.

AB - We prove a new extension result for QB-rings that allows us to examine extensions of rings where the ideal is purely infinite and simple. We then use this result to explore various constructions that provide new examples of QB-rings. More concretely, we show that a surjective pullback of two QB-rings is usually again a QB-ring. Specializing to the case of an extension of a semi-prime ideal I of a unital ring R, the pullback setting leads naturally to the study of rings whose multiplier rings are QB-rings. For a wide class of regular rings, we give necessary and sufficient conditions for their multiplier rings to be QB-rings. Our analysis is based on the study of extensions and the use of nonstable K-theoretical techniques. © Springer 2005.

KW - Exchange ring

KW - Multiplier ring

KW - Purely infinite simple ring

KW - QB-ring

U2 - https://doi.org/10.1007/s10468-004-5767-x

DO - https://doi.org/10.1007/s10468-004-5767-x

M3 - Article

SN - 1386-923X

VL - 8

SP - 75

EP - 97

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

ER -

Extensions and pullbacks in QB-rings

Abstract

Keywords

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