Zero is a regular ring or it is not?

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In commutative algebra, a regular ring is a commutative Noetherian ring, such that the localization at every prime ideal is a regular local ring: that is, every such localization has the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension.

In view of this definition, is it true to say the ring $0$ is regular?

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The zero ring is regular by vacuous truth. There is no prime ideal which witnesses non-regularity. Geometrically, the empty scheme is regular. More generally, any smooth scheme is regular, and the empty scheme is also smooth.