Krull dimension [SEP] named after
Krull dimension
In commutative algebra, the Krull dimension of a commutative ring "R", named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.
The Krull dimension has been introduced to provide an algebraic definition of the dimension of an algebraic variety: the dimension of the affine variety
Jaffard ring
In mathematics, a Jaffard ring is a type of ring, more general than a Noetherian ring, for which Krull dimension behaves as expected in polynomial extensions. They are named for Paul Jaffard who first studied them in 1960.
Formally, a Jaffard ring is a ring "R" such that the polynomial ring
where "dim" denotes Krull dimension. A Jaffard ring that is also an integral domain is called a Jaffard domain.
The Jaffard property is satisfied by any Noetherian ring "R"