free module

noun

A module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)

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Meanings

nounfree module (plural free modules)

plural free modules

  1. algebraA module that has a basis. Equivalently, a module consisting of n-tuples of ring elements with no extra identities. (Then the number n is said to be its rank.) Equivalently, a direct sum whose summands are all the same ring. (The quantity of summands may be more than two.)
Cite this entry
APA

free module. (n.d.). In WatkinsX Dictionary. Retrieved November 3, 2026, from https://dictionary.watkinsx.com/word/free%20module

MLA

“free module.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/free%20module. Accessed November 3, 2026.

Chicago

WatkinsX Dictionary, s.v. “free module,” accessed November 3, 2026, https://dictionary.watkinsx.com/word/free%20module.

Source: free module on Wiktionary, CC BY-SA 4.0.