I'm trying to understand something in my notes here....(adsbygoogle = window.adsbygoogle || []).push({});

So if we call the real part of the complex algebra 'even' and the imaginary part 'odd' then this graded algebra is communitive but NOT graded commutative. so ab = ba for all a and b in C.

If we call the whole complex algebra 'even' and only zero (also the only element in the intersection) to be odd then it would be graded commutative.

so ab = (-1)^(|b|*|a|)*ba

but if the whole of C is even, won't the parity of |b| and |a| always be zero and therefore the multiplication would just be normal commutative?

P.S. The whole idea of grading is still uneasy with me (obviously..)

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# The complex algebra graded by Z-2

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