@misc{10498/16100,
year = {2012},
month = {1},
url = {http://hdl.handle.net/10498/16100},
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.

As applications of these results, a uniqueness result for the Toeplitz algebra of a directed graph and characterizations of when crossed products of a ring by a single automorphism and fractional skew monoid rings of a single corner isomorphism are simple, are obtained.},
keywords = {Cuntz–Pimsner rings},
keywords = {Simplicity},
keywords = {Invariant cycles},
keywords = {Condition (L)},
keywords = {Cuntz–Krieger uniqueness},
keywords = {Toeplitz rings},
keywords = {Leavitt path algebras},
keywords = {Crossed products},
keywords = {Fractional skew monoid rings},
title = {Simple Cuntz-Pimsner rings},
doi = {10.1016/j.jalgebra.2012.08.005},
author = {Carlsen, T.M. and Ortega, E. and Pardo Espino, Enrique},
}