Abel's irreducibility theorem

proper noun

A field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x).

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

proper noun
  1. mathematicsA field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x).

Origin

Described in 1829 by Niels Henrik Abel.

Full word history & related roots →
Cite this entry
APA

Abel's irreducibility theorem. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Abel's%20irreducibility%20theorem

MLA

“Abel's irreducibility theorem.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Abel's%20irreducibility%20theorem. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Abel's irreducibility theorem,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Abel's%20irreducibility%20theorem.

Source: Abel's irreducibility theorem on Wiktionary, CC BY-SA 4.0.