Minimal polynomial (field theory)

Minimal polynomial (field theory)
Tag	`0VX9EP2GS8`
URI	`m2://0VX9EP2GS8`
Aliases	`minimal-polynomial`
Kind	concept
Writing	W1 stated
MSC	12F05
Same as	Wikidata Q2242730 Wikipedia Minimal polynomial (field theory)

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Summary

Let $a$ be algebraic over a field $K$ . The minimal polynomial of $a$ over $K$ is the monic polynomial of smallest degree in $K[x]$ that has $a$ as a root. The definition of the minimal polynomial states it.

What this node needs for W2

edge instance_of in: at least two examples (0 of 2)
edge not_instance_of in: at least one non-example (0 of 1)
edge specializes both: the more general notions and the special cases (0 of 1)

The writing levels say how complete the text of a node is. They do not measure its truth.

Sources

Web https://en.wikipedia.org/wiki/Minimal_polynomial_(field_theory), lead section

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Definitions

Minimal polynomial of an algebraic element 0GK1WB9R98