Distributivity and Associativity for 32/64bit signed integers

Question

I'm looking into 32/64bit signed integers and their algebraic properties. I am quite sure that the the three operators +, - and * fulfill the distributive and associative property (integer division does not because of the information loss) even though we have some kind of information loss due to wrapping of positive <-> negative numbers.

What I'm looking for is some kind of academic publication (if it is not too trivial) that addresses this issue and provides some proof or counterexample.

off-site resource recommendations are explicitly off-topic per [help/on-topic]. See http://meta.programmers.stackexchange.com/questions/6483/why-was-my-question-closed-or-down-voted/6487#6487 — gnat, Sep 30 '14 at 12:12
@gnat So it would be ok, to rephrase my question and not ask for offsite-links? — Artemis, Sep 30 '14 at 12:38
This question appears to be off-topic because it is about the mathematical properties of numbers. — , Sep 30 '14 at 15:55

score 0 · Accepted Answer · edited Apr 13 '17 at 12:19

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Integers modulo n (ℤ/nℤ) with addition and multiplication form a Commutative Ring, where multiplication distributes over addition. If n is prime, they even form a finite field.

I don't see why subtracting n/2 from every number (to make it signed) would necessarily change that.

For a definitive answer, Mathematics.SE is probably the better audience.

edited Apr 13 '17 at 12:19

Community

1

answered Sep 30 '14 at 12:56

Jörg W Mittag

103,514

Thanks. This supports my assumption. I'll have a look at math.SX. – Artemis Oct 01 '14 at 10:03

Distributivity and Associativity for 32/64bit signed integers

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