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WDMultiplication modulo n

Definition·D116

Multiply residue classes by multiplying representatives and taking the class of the result.

For and residue classes in (D114), multiplication is given on representatives by for , with on the right the multiplication of integers.
In words
The product of two residue classes is the class of the product of any chosen representatives.
Never needed: F03 · F04 · F05 · F06 · F08 · F10 · F11 · F12 · F13 · A03 · A04 · A05 · A07 · A08 · A09 (computed from the citation graph, not asserted).

Remarks

Well defined: by L74, if and then , so the result does not depend on the representatives chosen. Together with addition this makes a commutative ring with unity (T59). Modulo : . Unlike in , a product of nonzero classes can be zero: modulo , .

Used by