Nonzero central idempotents in G-graded rings have finite support when G is abelian or the grading satisfies a one-sided non-annihilation condition, generalizing Bass-Burns results to non-commutative non-unital settings.
de Cornulier, Infinite conjugacy classes in groups acting on trees,Groups Geom
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Central idempotents in group-graded rings
Nonzero central idempotents in G-graded rings have finite support when G is abelian or the grading satisfies a one-sided non-annihilation condition, generalizing Bass-Burns results to non-commutative non-unital settings.