Abstract

In this paper we introduce the concept of purely infinite rings, which in the simple case agrees with the already existing notion of pure infiniteness. We establish various permanence properties of this notion, with respect to passage to matrix rings, corners, and behaviour under extensions, so being purely infinite is preserved under Morita equivalence. We show that a wealth of examples falls into this class, including important analogues of constructions commonly found in operator algebras. In particular, for any (s-) unital $K$-algebra having enough nonzero idempotents (for example, for a von Neumann regular algebra) its tensor product over $K$ with many non-simple Leavitt path algebras is purely infinite.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 563-610
Launched on MUSE
2010-06-05
Open Access
No
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