We give examples that provide negative answers to three questions about abstract factorization posed by Anderson and Frazier. We show that (1) an atomic do- main need not be τ-atomic for τ divisive, (2) an atomic domain need not be a comaximal factorization domain (CFD) and (3) for τ divisive, a nonzero nonunit of a τ-UFD need not be a τ-product of τ-primes. Along the way, we generalize the theorem of Anderson and Frazier that a UFD is a τ-UFD for τ divisive (with a simplied proof), and we demonstrate a method for constructing domains with no pseudo-irreducible elements.
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