High Quality Content by WIKIPEDIA articles! In operator algebras, a uniformly hyperfinite, or UHF, algebra is one that is the closure, in the appropriate topology, of an increasing union of finite dimensional full matrix algebras. A UHF C*-algebra is the direct limit of an inductive system {An, ?n} where each An is a finite dimensional full matrix algebra and each ?n : An ? An+1 is a unital embedding. Suppressing the connecting maps, one can write A = overline {cup_n A_n}. If A_n simeq M_{k_n} (mathbb C), then r kn = kn + 1 for some integer r and phi_n (a) = a otimes I_r, where Ir is the identity in the r x r matrices. The sequence ...kn|kn + 1|kn + 2... determines a formal product, delta(A) = prod_p p^{t_p}, where each p is prime and tp = sup {m|pm divides kn for some n}, possibly zero or infinite.

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