Let Λ be a finite dimensional basic algebra over an algebraically closed field k. Let P be a finitely generated left Λ module and e an idempotent of Λ such that addP = addΛe. we denote by addP (respectively, addΛe) the category of all direct summands of finite direct sums of copies of P(respectively, Λe). How can I prove that |Λ/e| = |Λ|-|P|, where |X| denotes the number of nonisomorphic indecomposable direct summands of X?
2026-02-27 16:15:16.1772208916
Prove that |Λ/e| = |Λ|-|P|
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