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The ring of formal polynomials in an indeterminate over a coefficient ring .
wp-polynomial-ringmilne-fields-galois-theorystacks-algebra-textEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Form finite formal sums in a variable with coefficients in the ring.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
milne-fields-galois-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
A polynomial ring over a commutative coefficient ring is itself commutative.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
milne-fields-galois-theorystacks-algebra-textwp-comm-ringThis is an authored directed relation from the source endpoint to the target endpoint.
Choose a polynomial or family over the base field and a field generated by all of its roots. The resulting splitting field is unique up to base-field isomorphism, not as a literally canonical subfield without an ambient algebraic closure.
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
milne-fields-galois-theory