0_0 ${\displaystyle e^{i\pi }}$ This user is amathematician. PhD This user has aDoctor of Philosophy degree inMathematics. This userparticipates in WikiProject Mathematics. This user enjoyschess. This user listens toindustrial. This user enjoysspeedcubing and has a personal record of 0'0"45. This user has been on Wikipedia for19 years, 7 months and 20 days.

WPM-MainWPM-TalkWPM-Desk/Bibliography/Cold storage

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

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

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

• Contribute "trivial extension" material atdual 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

• Q1:In theKissing 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 isr, then the central sphere has radius${\displaystyle r(\sqrt{1+{\varphi }^2}-1)}$.

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• Wikipedians with PhD degrees
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