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Let      A A       be a commutative ring, and let      X X       = projective      r r      -space over      A A      . Then we prove that      K 1 {K_1}       of the category of locally free sheaves of finite type on      X X       is isomorphic to the direct sum of      r + 1 r + 1       copies of      K 1 ( A ) {K_1}(A)      .

𝐾₁ of projective 𝑟-spaces