The definition of UFD requires that each non-unit, non-zero element to have a finite, unique factorization of irreducibles. But is it possible for a non-unit, non-zero element to also be a product of infinitely many non-unit elements? I would guess no since each of those non-unit element may be written as product of irreducibles, implying the original element being an infinite product of irreducibles. Am I right on this?
2026-04-03 14:25:00.1775226300
UFD: existence of an infinite factorization
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