User:Rschwieb

WPM-Main WPM-Talk WPM-Desk /Bibliography /Cold storage

/Sandbox /GA Discussion /Physics notes /Requiring identity table

Interests
Ring and module theory, mathematical physics, representation theory, applications of abstract algebra.

Contributed stuff
Articles:
 * Serial module, Uniform module, Dense submodule, Singular submodule, Hopfian object, minimal ideal, balanced module
 * Hopkins–Levitzki theorem, Double centralizer theorem, Jacobson's conjecture
 * Quasi-Frobenius ring, Semiprime ring, Kasch ring

Sections:
 * superfluous submodule, finitely cogenerated modules
 * full linear ring
 * idempotent element

Also put serious effort into:
 * Jacobson radical, Prime ideal, associated prime, Regular ideal
 * Matrix ring
 * Centralizer and normalizer
 * Algebraic structure
 * Irreducible ring

Random notes to self

 * Contribute "trivial extension" material at dual number
 * injective cogenerator, Morita duality
 * Hopkins' theorem
 * Maschke's theorem
 * highlight differences of comm/noncomm on RT page
 * maximal rings of quotients
 * Dedekind finite ring
 * /Read These, /Amusing
 * /Algebraic structure copy
 * LaTeX symbol tool link posted by Joel B. Lewis
 * Berkeley MGSA

Questions

 * Q1:In the Kissing number problem for three dimensions, I hadn't heard that there was extra space between the 12 spheres around the central sphere. Does anyone know if the radius of the surrounding spheres be uniformly increased so they are all mutually touching, while still touching the (unchanged) central sphere?  If so what is this new radius?
 * A1: If the radii of the surrounding spheres is r, then the central sphere has radius $$r(\sqrt{1+\phi^2}-1)\,$$.