Linear Associative Algebra

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[2421 2 ]. The denning equation of this case can be reduced to This gives a quintuple algebra which may be called (& 5 ), its multiplication table being* (ba 5 ) i j k I m k m j I m I -\-ern *In relative form, i = A : B + B : C+ A : E, j A : C, fc= D : B + E : F -f D : (? + eG : C+A :E, 1 = A :F, m D:C. By omitting the last term of fc and putting e = 1 we get (6b 5 ), and by omitting the last two terms of k we get (&c 5 ). [C. S. P. ] 90 PEIRCE : Linear Associative Algebra.
[2421 2 ]. The defin
...ing equation of this case can be reduced to = m.
This gives a quintuple algebra which may be called (66 5 ), its multiplication table being (bb 5 ) i j Jc I m m j I m m o [24213]. The defining equation of this case is This gives a quintuple algebra which may be called (6c B ), its multiplication table being (bc 5 ) i j 7c I m i j I j le m I m PEIRCE : Linear Associative Algebra. 91 [242 2 ]. The defining equation of this case is % = 0.
There are two cases : [242 2 1], when e B does not vanish ; [242 3 ], when e s vanishes.


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