09/03/2011, 07:22 PM
Hmm yes, I think you're right.
I think it may be pushing it to have it be commutative. Sadly we lose it's base changing properties.
But the original equation is intriguing, I'd really like to see if it would even be possible.
Off the bat we can rearrange it to make one the identity:
\( c\, \otimes_\mu\, 1 = c \)
and
\( 1\,\otimes_\mu\, c = 1 \)
we'd also get
\( 0\,\otimes_\mu\, c = 0 \)
I'd like to continue looking at this.
I think it may be pushing it to have it be commutative. Sadly we lose it's base changing properties.
But the original equation is intriguing, I'd really like to see if it would even be possible.
Off the bat we can rearrange it to make one the identity:
\( c\, \otimes_\mu\, 1 = c \)
and
\( 1\,\otimes_\mu\, c = 1 \)
we'd also get
\( 0\,\otimes_\mu\, c = 0 \)
I'd like to continue looking at this.