this post was submitted on 12 Mar 2025
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[–] kogasa@programming.dev 1 points 2 months ago (4 children)

There's not much coherent algebraic structure left with these "definitions." If Ωx=ΩΩ=Ω then there is no multiplicative identity, hence no such thing as a multiplicative inverse.

[–] Leate_Wonceslace@lemmy.dbzer0.com 1 points 2 days ago (3 children)

No; 1 is the multiplicative identity.

1Ω=Ω, and for all x in C 1x=x. Thus, 1 fulfills the definition of an identity.

[–] kogasa@programming.dev 2 points 2 days ago (2 children)

1 = Ω0 = Ω(Ω + Ω) = ΩΩ + ΩΩ = Ω + Ω = 0

so distributivity is out or else 1 = 0

[–] Leate_Wonceslace@lemmy.dbzer0.com 1 points 1 day ago (1 children)

Correct; multiplying by Ω doesn't distribute over addition.

[–] kogasa@programming.dev 1 points 1 day ago

Distributivity is a requirement for non associative algebras. So whatever structure is left is not one of those