Primordial element (algebra)
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In algebra, a primordial element is a particular kind of a vector in a vector space.
Definition[]
Let be a vector space over a field and let be an -indexed basis of vectors for By the definition of a basis, every vector can be expressed uniquely as
for some -indexed family of scalars where all but finitely many are zero.
Let
denote the set of all indices for which the expression of has a nonzero coefficient.
Given a subspace of a nonzero vector is said to be primordial if it has both of the following two properties:[1]
- is minimal among the sets where and
- for some index
References[]
- ^ Milne, J., Class field theory course notes, updated March 23, 2013, Ch IV, §2.
Categories:
- Algebra
- Vector spaces
- Vectors (mathematics and physics)
- Algebra stubs