Simple Cuntz-Pimsner rings

Abstract

Necessary and sufficient conditions for when every non-zero ideal in a relative Cuntz-Pimsner ring contains a non-zero graded ideal, when a relative Cuntz-Pimsner ring is simple, and when every ideal in a relative Cuntz-Pimsner ring is graded, are given. A "Cuntz-Krieger uniqueness theorem" for relative Cuntz-Pimsner rings is also given and condition (L) and condition (K) for relative Cuntz-Pimsner rings are introduced.

References in corpus (2)

• Ideal structure of $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences
• Algebraic Cuntz-Pimsner rings

Cited by in corpus (2)

• Topological freeness for $C^{\ast }$-correspondences
• $\mathbb{Z}$-graded rings as Cuntz-Pimsner rings