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This analysis shows properties relating to free summands in finitely generated modules over local rings, indicating implications for endomorphism rings.
Let R be a local ring and let M be a finitely generated R-module. Appealing to the natural left module structure of M over its endomorphism ring and corresponding center Z(EndR(M)), we study when various homological properties of M are sufficient to force M to have a nonzero free summand. Consequences of our work include a partial converse to a well-known result of Lindo describing Z(EndR(M)) when M is faithful and reflexive, as well as some applications to the famous Huneke-Wiegand conjecture.
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Dey et al. (2025) studied this question.
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