this post was submitted on 12 Mar 2025
588 points (98.2% liked)

Comic Strips

16806 readers
2073 users here now

Comic Strips is a community for those who love comic stories.

The rules are simple:

Web of links

founded 2 years ago
MODERATORS
 
you are viewing a single comment's thread
view the rest of the comments
[–] CompassRed@discuss.tchncs.de 1 points 3 days ago

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.