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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...
Replacing invertibility with quasi-invertibility in Bass' first stable range condition we discover a new class of rings, the QB-rings. These constitute a considerable enlargement of the class of rings with stable rank one (B-rings) and include examples like End F (V), the ring of endomorphisms of a vector space V over some field F, and B(F), the ring of all row- and column-finite matrices...
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