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Primordial element (algebra)

释义

References

In algebra, a primordial element is a particular kind of a vector in a vector space. Let V be a vector space over a field k and fix a basis for V of vectors for . By the definition of a basis, every vector v in V can be expressed uniquely as

Define , 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:^[1]

is minimal among the sets , and
for some i

References

1. ^Milne, J., Class field theory course notes, updated March 23, 2013, Ch IV, §2.

1 : Algebra

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