What is...the calculus of ideals?
Goal.
Explaining basic concepts of (a classical course in) algebra in an intuitive way.
This time.
What is...the calculus of ideals? Or: Ideals are like numbers.
Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.
Nonsense.
On the slide “Example. Z/4Z[X ] with X 2 = 0” the element 2+3X is missing in the middle set.
On the “Another slick illustration” is a sum_{finite} missing in the definition of IJ. It should be IJ={sum_{finite} ij}.
Material used.
https://en.wikipedia.org/wiki/Ideal_(...)
https://en.wikipedia.org/wiki/Categor...
Semiring.
https://en.wikipedia.org/wiki/Semiring
Lattice.
https://en.wikipedia.org/wiki/Lattice...)
Ideals and lattices.
https://unapologetic.wordpress.com/20...
https://unapologetic.wordpress.com/20...
Types of ideals.
https://en.wikipedia.org/wiki/Ideal_(...
#algebra
#galoistheory
#mathematics