DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-06

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Tor from a projective resolution of the left module

Definition

For a right $R$ -module $N$ and a left $R$ -module $M$ with a specified projective resolution $P_{∙} ↠ M$ , define the left-resolution construction ${Tor}_{n}^{R, P} (N, M) : = H_{n} (N \otimes_{R} P_{∙}) .$ The datum $P$ remains in the notation until the balance and change-of-resolution results prove that it may be suppressed.

Depends on

Dependency tree · 2 levels

Sources

Weibel, An Introduction to Homological Algebra