Algebra I¶
Bourbaki, N. (1974). Algebra I: Chapters 1-3. Addison-Wesley.
Cited by¶
1 citation across 1 artifact.
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Primes¶
- Monoid
- Each axiom shrinks the population of instances and enlarges the theorems holding of every survivor, and monoid is the rung at which every finite sequence of carrier elements — the sequence of length zero included — acquires a single well-defined product.
This sourceEstablishes the magma-semigroup-monoid-group hierarchy, the general associativity theorem, and the empty-product convention that gives every finite sequence, the empty one included, a well-defined product.
Supported in partVerified against the work's full text
Bourbaki defines monoid as associative unital magma and gives the empty family the identity as its composition, supporting the sequence-product half but not the axiom-trade-off framing.
“called the com- position of the empty family of elements”
- Each axiom shrinks the population of instances and enlarges the theorems holding of every survivor, and monoid is the rung at which every finite sequence of carrier elements — the sequence of length zero included — acquires a single well-defined product.
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