Jacobson radical

noun

The operation that produces (from a given ring) the ideal of elements which annihilates all simple modules (over the given ring); the result of this operation. The Jacobson radical of a ring R is denoted J(R).

Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

nounJacobson radical (plural Jacobson radicals)

plural Jacobson radicals

  1. ring theorymathematicsThe operation that produces (from a given ring) the ideal of elements which annihilates all simple modules (over the given ring); the result of this operation. The Jacobson radical of a ring R is denoted J(R).
Cite this entry
APA

Jacobson radical. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Jacobson%20radical

MLA

“Jacobson radical.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Jacobson%20radical. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “Jacobson radical,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Jacobson%20radical.

Source: Jacobson radical on Wiktionary, CC BY-SA 4.0.