From wikipedia I have accrossed this claim "The Krull dimension of the zero ring is typically defined to be either ${\displaystyle -\infty } $ or ${\displaystyle -1} $. The zero ring is the only ring with a negative dimension " . Now my question here is :Why krull dimension of zero ring defined to be negative or just a convention ?
2026-03-25 06:05:27.1774418727
Why Krull dimension of zero ring defined to be negative or it is just a convention?
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The least upper bound of the length of a chain of prime ideals in the zero ring is $-\infty$, since the zero ring has no prime ideals.