For a vector space, this value equals the cardinality of a basis.
For a ring, this quantity is the least upper bound of its prime ideals and is named after Krull. For a vector space, this value equals the cardinality of a basis. Another version of this quantity is given by the quotient of the logarithms of the space-scaling rate and the log of the linear scaling rate; that form of this quantity is named for Felix Hausdorff, and gives non-integer values for fractals. This value is equal to the number of coordinates required to locate a point in a given space, which is why spherical and cylindrical coordinate systems require three values, while polar coordinates re- quire two. Give this value which equals zero for a point and one for a line.
For a ring, this quantity is the least upper bound of its prime ideals and is named after Krull.
{dimensions} [or {dimensionality}; accept {rank}]