Krull dimension (1253 bytes)
2: ...mathematics)|ring]] ''R'', named after [[Wolfgang Krull]] ([[1899]] - [[1971]]), is defined to be the num...
6: ...nclusions in this chain, that is, 3. In fact the dimension of this ring is exactly 3.
8: ...phrasing this definition is to say that the Krull dimension of ''R'' is the largest [[height (ring theory)|he...
10: ...d domain]]s and [[discrete valuation ring]]s have dimension one.
12: ...2''k'' + 1. If ''R'' is ''Noetherian'', then the dimension of ''R''[''x''] will be exactly ''k'' + 1.

Krull (2187 bytes)
1: Krull ([[1983]]) is a heroic fantasy film directed by [...
11: The world of Krull is invaded by The Beast and his army of Slayers, ...

Wolfgang Krull (282 bytes)
1: ...[Krull dimension]], the [[Krull topology]], and [[Krull's principal ideal theorem]] are named.
7: [[Category:1899 births|Krull]]
8: [[Category:1971 deaths|Krull]]
9: [[Category:Mathematicians|Krull]]

Krull's principal ideal theorem (769 bytes)
1: ...em is sometimes referred to by its German name, ''Krulls Hauptidealsatz''.
5: ... not principal, and the result is often called '''Krull's height theorem'''. It says, if ''R'' is a Noet...

La Dimension X (176 bytes)
1: '''La Dimension X''' is a [[French science fiction]] [[novel]] wr...

Fifth Dimension (1764 bytes)
1: '''The 5th Dimension''' is an [[United States| American]] [[popular mu...
10: Some of the songwriters popularised by The 5th Dimension later went on to [[careers]] of their own, especi...
23: *''The 5th Dimension/Live!'' (1971)
38: ...album]] called '''[[Fifth Dimension_(album)|Fifth Dimension]]'''.

Dimension (6632 bytes)
2: ...ticle is about. Also, in [[science fiction]], a "dimension" can also refer to a separate world or plane of e...
4: ==Physical dimensions==
6: ...irely sensible) to consider this as three spatial dimensions and one of time. We can move up-or-down, north-o...
8: ...n'. It is somewhat different to the three spatial dimensions in that there is only one of it, and movement se...
10: ...that the universe measured along these additional dimensions is subatomic in size.

Dimension X (785 bytes)
1: '''''Dimension X''''' was an [[old-time radio]] program broadcas...
3: Dimension X was the first notable adult [[science fiction]]...
8: Dimension X lasted only one year, but the later [[X Minus O...

VC dimension (2857 bytes)
1: ...he '''VC dimension''' (for '''Vapnik Chervonenkis dimension''') is a measure of the [[capacity]] of a [[class...
7: ...tion of capacity, called the VC dimension. The VC dimension of a model <math>f</math> is the maximum <math>h<...
9: The VC dimension has utility in statistical learning theory, becau...
15: ...ath>1-\eta</math>, where <math>h</math> is the VC dimension of the classification model, and <math>N</math> i...
19: ...p://www-2.cs.cmu.edu/~awm/tutorials/vcdim.html VC dimension tutorial]

Dimension 5 (314 bytes)
1: '''Dimension 5''' are [[Kerry Palmer]], [[Nick Wenham]], [[Jud...
5: *[[Transdimensional]] ([[Intastella Records]] [[1997]])

Vowel dimension (1196 bytes)
1: A '''vowel dimension''' is an aspect of a [[vowel]]'s pronunciation, i...
3: ...patial movement in two physical dimensions. These dimensions can be extraordinarily complex in themselves; th...
5: ...wedish]] mean that these dialects exhibit a three-dimensional vowel system, with non-binary oppositions in ea...

Isoperimetric dimension (6407 bytes)
1: ... the [[topological dimension]] or the [[Hausdorff dimension]] which compare different ''local behaviors'' aga...
3: ...face area, and this is not what the isoperimetric dimension is about. The question we will ask is, what is ''...
7: ... about a manifold ''M'' that it satisfies a ''d''-dimensional '''isoperimetric inequality''' if for any open ...
11: ...dimensional volume and area refers to (''n'' - 1)-dimensional volume. ''C'' here refers to some constant, whi...
13: ... on all ''d''-s such that ''M'' satisfies a ''d''-dimensional isoperimetric inequality.

The 7th Dimension (904 bytes)
3: ...y been aired on other BBC stations. A few Seventh Dimension shows are new commisions.
9: *[http://www.bbc.co.uk/bbc7/drama/7thdimension.shtml Official site]

Dimension Films (347 bytes)
1: '''Dimension Films''', a subsidiary of ''[[Walt Disney]]'' has...

Hausdorff dimension (15549 bytes)
1: ...called the '''capacity dimension''' or '''fractal dimension'''.
3: ...wo-dimensional. As one would expect, topological dimension is always a [[natural number]].
5: ... Hausdorff dimension gives another way to define dimension, which takes the metric into account.
7: ...00px|Sierpinski Gasket. A space having fractional dimension ln 3 / ln 2, which is approximately 1.58]]
9: ...rff dimension refines the concept of topological dimension and also relates it to other properties of the sp...

Dimension table (689 bytes)
1: A '''dimension table''' is a [[data warehousing]] concept. It is...
3: ...ndidate key]]s (normally [[primary key]]s) in the dimension tables.
5: The dimension tables contain [[attribute]]s or (fields) used to...

Fourth dimension (6171 bytes)
1: ... [[special relativity]], in addition to the three dimensions of [[space]], [[time]] is included to form [[spa...
3: ...mensions of length, width, and height. The fourth dimension is said to be at right angles to these three, and...
6: ...ng intuitive concepts to build up a definition of dimension.
8: A ''[[Point (geometry)|point]]'' is a zero-dimensional object. It has no extension in space, and no pr...
10: ... the zero vector), we get a single line, with one dimension of length. All the vectors that describe points o...

4th Dimension (1048 bytes)
1: ...nt Ribardière]] has started to develop the '''4th Dimension''' (or just '''4D''') relational [[ database man...
5: ...1993, 4D Server, the client/server version of 4th Dimension started and since 1995, 4D is available as a cro...
7: The actual version of 4th Dimension, 4D 2004 is the first product that allows develop...
9: 4th Dimension is localized in different languages as English, F...

Northern dimension (682 bytes)
1: The '''Northern dimension''' is an initiative in the [[European Union]] reg...

Compact dimension (381 bytes)
1: ...int almost instantaneously, and the fact that the dimension is smaller than the smallest particle means that ...

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