In the interest of closing some terrifying gaps in my budget I am selling this piece, the limit does not exist, for $125 plus shipping

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Did everyone see the excellent point by @noetherianthing.bsky.social that if b=c=1 (i.e., if the algebra has a multiplicative identity) then a=-a and it's actually associative? So even loops (or loop algebras?) can't get anything weird here; we'd have to resort to quasigroup algebras

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I want malassociativity to be an interesting thing now because I want to say malassociative malgebra.

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For various weird and "online too much today" reasons I was wondering about objects with a binary operation that is skew-associative (assuming there is an addition with identity and inverses): (a*b)*c = -(a*(b*c)) How bad is this? Like, is it so bad it's impossible?

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Thanks to @noncommutativity.bsky.social for planting the seed of "malassociative algebra" in my head

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