en>Dewritech: clean up, typo(s) fixed: obselete → obsolete using AWB

2013-10-09T14:38:32Z

clean up, typo(s) fixed: obselete → obsolete using AWB

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{{refimprove|date=January 2013}}

In [[algebra]], a '''primordial element''' is a particular kind of a [[Vector (mathematics and physics)|vector]] in a [[vector space]]. Let ''V'' be a vector space over a [[field (mathematics)|field]] ''k'' and fix a [[Basis (linear algebra)|basis]] for ''V'' of vectors <math>e_i</math> for <math>i \in I</math>. By the definition of a basis, every vector ''v'' in ''V'' can be expressed uniquely as
:<math>v = \sum_{i \in I} a_i(v) e_i.</math>
Define <math>I(v) = \{ i \in I \mid a_i(v) \ne 0 \}</math>, the set of indices for which the expression of ''v'' has a nonzero coefficient. Given a subspace ''W'' of ''V'', a nonzero vector ''w'' in ''W'' is said to be "primordial" if it has the following two properties:<ref>Milne, J., [http://www.jmilne.org/math/CourseNotes/cft.html Class field theory course notes], updated March 23, 2013, Ch IV, §2.</ref>
#<math>I(w)</math> is minimal among the sets <math>I(w')</math>, <math>0 \ne w' \in W</math> and
#<math>a_i(w) = 1</math> for some ''i''.

== References ==
{{reflist}}

[[Category:Algebra]]

{{algebra-stub}}

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en>Dewritech: clean up, typo(s) fixed: obselete → obsolete using AWB