Moduloid - Abelian Unital Magma

[Tom Piper]

Magma as the mathematical object may be too big to be dealt with.
However I found the magma which is commutative and has the unit element
has some interesting properties which might be applicable to algebra
and topology. For details, please visit;
http://geocities.com/tontokohirorin/mathematics/moduloid/moduloid2.htm

 

[matt grime]

For those wondering, like me:

A magma is simple a set with a binary operation into itself (ie something like an operation on equivalence classes of binary trees indexed by the underlying set). Examples of which are, groups, groupoids, monoids etc.

The link is to a nicely presented page, though I don't have time to read it to see what it is saying. Perhaps a summary? An abstract, here?

 

[Tom Piper]

For those wondering, like me:

A magma is simple a set with a binary operation into itself (ie something like an operation on equivalence classes of binary trees indexed by the underlying set). Examples of which are, groups, groupoids, monoids etc.

The link is to a nicely presented page, though I don't have time to read it to see what it is saying. Perhaps a summary? An abstract, here?

Thank you for your comment. My website is regarding a generalization of residue arithmetic, in short. You may imagine the residue space in the linear space. I substituted the linear space by some quotient spaces such as sphere, real projective plane, Klein bottle, etc. Then I found the addition induced in that space does not form group, or even monoid in some cases. By discretizing that space, a finite set - or magma - is obtained. I thought that magma may characterize the quotient space in a certain meaning.

 

[Tom Piper]

I updated the webpage with implementing software for calculating the moduloid (or magma) for the cases of torus, sphere, real projective plane, and Klein Bottle as,
http://geocities.com/tontokohirorin/mathematics/moduloid/moduloid2.htm

 

[Tom Piper]

The discussion of a chaotic map different from the horseshoe map in the viewpoint of quotient space is newly added in the following site;
http://geocities.com/tontokohirorin/mathematics/moduloid/moduloid2.htm