List of Abstract Algebra Topics - Non-associative Systems

Non-associative Systems

General
  • Associative property, Associator
  • Magma (algebra)
    • Loop (algebra), Quasigroup
  • Nonassociative ring, Non-associative algebra
    • Universal enveloping algebra
    • Lie algebra (see also list of Lie group topics and list of representation theory topics)
    • Jordan algebra
    • Alternative algebra
    • Power associativity
    • Flexible algebra
Examples
  • Cayley–Dickson construction
    • Octonions
    • Sedenions
  • Virasoro algebra

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    The only people who treasure systems are those whom the whole truth evades, who want to catch it by the tail. A system is just like truth’s tail, but the truth is like a lizard. It will leave the tail in your hand and escape; it knows that it will soon grow another tail.
    Ivan Sergeevich Turgenev (1818–1883)