Constructs a nearly atomic non-atomic integral domain and strengthens the FFD characterization to nearly atomic plus IDF, while showing almost atomicity fails.
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In the almost Dedekind domain D built from field F and prime p, the paper gives conditions for irreducibles in D_n to stay irreducible in D, shows D has no irreducibles for algebraically closed F or finite F of characteristic p, and for F=Q and p=2 proves every nonzero nonunit factors into countably
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On near atomicity and a characterization of the FF property
Constructs a nearly atomic non-atomic integral domain and strengthens the FFD characterization to nearly atomic plus IDF, while showing almost atomicity fails.
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Factorization in almost Dedekind domain
In the almost Dedekind domain D built from field F and prime p, the paper gives conditions for irreducibles in D_n to stay irreducible in D, shows D has no irreducibles for algebraically closed F or finite F of characteristic p, and for F=Q and p=2 proves every nonzero nonunit factors into countably