A group is not an algebra. A group consists of a single associative binary operation with an identity element and inverses for each element.

A ring is an abelian (commutative) group under addition, along with an additional associative binary operation (multiplication) that distributes over addition. The additive identity is called zero.

A field is a ring in which every nonzero element has a multiplicative inverse.

A vector space over a field consists of an abelian group (the vectors) together with scalar multiplication by elements of the field, satisfying distributivity and compatibility conditions.

A non-associative algebra is a vector space equipped with a bilinear multiplication operation that distributes over vector addition and is compatible with scalar multiplication.

An (associative) algebra is a non-associative algebra whose multiplication operation is associative.

You can read more about these definitions online and in textbooks - these are standard definitions. If you are using different definitions, then it would help your case to provide them so we can better understand your claims.

There’s a general negative attitude towards chromium browsers due to some anticompetitive practices pulled by Google in addition to privacy concerns and probably some more issues I’m not aware of. So that includes chrome, but also edge and most other chromium based browsers.

The definition I’m aware of for non associative algebras has them distributive by default, so I believe the chain of equations is valid.

Interesting. I think it isn’t unital either otherwise Ω=0.

0=Ω+Ω=Ω+ΩΩ=Ω(1+Ω)=ΩΩ=Ω