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...

ring Krull dimension Krull ring Krull topology Krull–Azumaya theorem Krull–Schmidt category Krull–Schmidt theorem Krull's intersection theorem Krull's principal...

A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described...

A five-dimensional space is a space with five dimensions. In mathematics, a sequence of N numbers can represent a location in an N-dimensional space....

In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (coordinates)...

Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible...

ring is a commutative ring such that the homological dimension is equal to the Krull dimension. The theory is simpler for commutative rings that are...

In mathematics, a fractal dimension is a term invoked in the science of geometry to provide a rational statistical index of complexity detail in a pattern...

Lebesgue covering dimension or topological dimension of a topological space is one of several different ways of defining the dimension of the space in a...

inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These...

This is a consequence of the Krull intersection theorem. Fully bounded Noetherian rings Noetherian rings with Krull dimension 1 Noetherian rings satisfying...

ideal. Thus any commutative local ring with Krull dimension zero is Jacobson, but if the Krull dimension is 1 or more, the ring cannot be Jacobson. (Amitsur...

In mathematics, a Euclidean plane is a Euclidean space of dimension two, denoted E 2 {\displaystyle {\textbf {E}}^{2}} or E 2 {\displaystyle \mathbb {E}...

Carl Krull (born 1975) is a contemporary Danish artist. Best known for his "seismic" approach to sculptural drawing and painting, Krull works in various...

commutative ring to its internal ring structure, particularly its Krull dimension and depth. The following list given by Melvin Hochster is considered...

As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves...

sequence. Krull ring A Krull ring (or Krull domain) is a ring with a well behaved theory of prime factorization. Krull dimension See dimension. Laskerian...

generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or...

of the Krull dimension of a ring, first for Noetherian rings before moving on to expand his theory to cover general valuation rings and Krull rings. To...

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...

space of dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1. Equivalently...

Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension (1994, ISBN 0-19-286189-1) is a book by Michio Kaku, a theoretical physicist...

2019. Rojas, Rodrigo (17 September 2019). "Cecilia Krull, la voz por detrás de la canción de "La casa de papel"" (in Spanish). vos.lavoz.com.ar. Archived...

at a prime ideal. The concept of local rings was introduced by Wolfgang Krull in 1938 under the name Stellenringe. The English term local ring is due...

environmental, economic, and social. Many definitions emphasize the environmental dimension. This can include addressing key environmental problems, including climate...

nonzero finitely generated R-module M is at most the Krull dimension of M (also called the dimension of the support of M). Given an integral domain R {\displaystyle...

for planes of rotation is in describing more complex rotations in four-dimensional space and higher dimensions, where they can be used to break down the...

which is an algebraic notion of dimension that is related to but different from the geometric notion of Krull dimension. Moreover, in certain circumstances...

{\displaystyle d(x,y)=\|x-y\|} ), the last property can be made stronger using the Krull sharpening to: ‖ x + y ‖ ≤ max { ‖ x ‖ , ‖ y ‖ } {\displaystyle \|x+y\|\leq...

partner and children. 2023 The Butch Closet, Craig Krull Gallery, Santa Monica, CA 2018 Swagger, Craig Krull Gallery, Santa Monica, CA 2018 The Great Outdoors...