Module Theory

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3 domain-specific abstractions whose origin domain is Module Theory.

• Free presentation — An exact sequence of free modules mapping generators and relations onto a module.
• Indecomposable module — A nonzero module that cannot be expressed as a direct sum of two nonzero submodules.
• Principal indecomposable module — An indecomposable direct summand of the regular module of a ring, equivalently an indecomposable projective cyclic module under standard hypotheses.