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Three of Katsura's papers have "Ideal structure" or "Ideal structures" in the title.

A quick search reveals more papers defining or referring to the notion of a Katsura ideal.

Three of Katsura's papers have "Ideal structure" or "Ideal structures" in the title.

A quick search reveals more papers defining or referring to the notion of a Katsura ideal.

See in particular the paragraph across pages 15 and 16 in the memoir Operator Algebras for Multivariable Dynamics by Kenneth R. Davidson and Elias G. Katsoulis (the link is to Google books).