%0 Journal Article 
%A Carlsen, T.M.
%A Ortega, E.
%A Pardo Espino, Enrique
%T Simple Cuntz-Pimsner rings
%D 2012
%@ 0021-8693
%U http://hdl.handle.net/10498/16100
%X 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.
%K Cuntz–Pimsner rings
%K Simplicity
%K Invariant cycles
%K Condition (L)
%K Cuntz–Krieger uniqueness
%K Toeplitz rings
%K Leavitt path algebras
%K Crossed products
%K Fractional skew monoid rings
%~ Universidad de Cádiz