A rooted tree module over a zero-relation algebra is indecomposable (char K not 2) exactly when the defining tree has no nontrivial idempotent self-map, giving checkable splitting and construction algorithms.
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Rooted tree modules
A rooted tree module over a zero-relation algebra is indecomposable (char K not 2) exactly when the defining tree has no nontrivial idempotent self-map, giving checkable splitting and construction algorithms.