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We have previously [1] defined regular n-linear mappings and shown that they may be expressed in at most one way as direct products of indecomposable mappings. We wish to extend this result to the case in which n is co or, more generally, any transfinite ordinal a of class 2. If Hi (i<a) and K, which we sometimes denote by Ha, are groups, f is a regular a-linear mapping on Hi (i<a) to K, denoted by

The unique decomposition of regular 𝜔-linear mappings as direct products