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In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A with 1, the projective line P(A) over A consists of points identified by homogeneous coordinates. Let U be the group of units of A; pairs (a,b) and (c,d) from A × A are related when there is a u in U such that ua = c and ub = d. This relation is an equivalence relation. A typical equivalence class is written U(a,b). P(A) = { U(a,b) : aA + bA = A }, that is, U(a,b) is in the projective line if the ideal generated by a and b is all of A.

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  • Projective line over a ring
  • 環上の射影直線
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  • 数学における環上の射影直線(しゃえいちょくせん、英: projective line over a ring)は体上の射影直線を一般化するものである。
  • In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A with 1, the projective line P(A) over A consists of points identified by homogeneous coordinates. Let U be the group of units of A; pairs (a,b) and (c,d) from A × A are related when there is a u in U such that ua = c and ub = d. This relation is an equivalence relation. A typical equivalence class is written U(a,b). P(A) = { U(a,b) : aA + bA = A }, that is, U(a,b) is in the projective line if the ideal generated by a and b is all of A.
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