2008/06/25 by Gonzalo Aranda Pino, Ken Goodearl, Pino, Gonzalo Aranda +6
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.48550/arxiv.0806.4156
arxiv created 2008/06/25 · openalex publication_date 2008/06/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 nonsimple Leavitt path algebras is purely infinite.