Abstract
Let FI(X, K) be the finitary incidence algebra of a poset X over a field K. In this short note we establish when FI(X, K) satisfies a polynomial identity and when its group of units U ( F I ( X , K ) ) satisfies a group identity. The Lie derived length of FI(X, K) and the derived length of U ( F I ( X , K ) ) are also determined.
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