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Encyclopedia > Multiplicative set

In mathematics, A set S is a multiplicative set if xy is in S whenever x and y both are in S.


Given a ring R, a multiplicative subset S of R is a multiplicative set such that 1 is in S.


  Results from FactBites:
 
Genotype-environmental interaction (1381 words)
Set Percent of GxE SS explained Cumulative --- --------------------------- ---------- 1 36.86 36.86 2 17.13 53.99 3 14.25 68.24 4 10.93 79.17 5 7.68 86.85 6 5.13 91.98 7 3.50 95.48 8 3.16 98.64 9 1.35 99.99 -----------------------------------------------
For the first set, the adjusted scores for the ten genotypes are 0.262, 2.011, -5.718, -0.526, 0.812, -0.387, 2.036, -0.976, 0.734, and 1.753.
suggested that the sum of squares of for set n of multiplicative components be allocated G + E - 1 - 2n degrees of freedom.
Field (mathematics) Summary (2054 words)
The ratio 0/1 is an additive identity, and the ratio 1/1 is a multiplicative identity.
The ratios a/b and -a/b are additive inverses, and a/b and b/a (a, b 0) are multiplicative inverses.
For a given field F, the set F(X) of rational functions in the variable X with coefficients in F is a field; this is defined as the set of quotients of polynomials with coefficients in F.
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