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Science
/ abstract algebra
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math
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Can you name the axioms which define the following objects?
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mockeldritch
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Below are a list of mathematical objects. Can you name the axioms which define them? To avoid repetition only distinct properties qualify.
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Group
GxG->G
A*(B*C) = (A*B)*C
for all g in G, g^-1 is in G
for some e and all g in G, e*g = g = g*e
Abelian Group
A*B = B*A
Vector Space
V + V -> V
a * V -> V
(V, +)
S
Ring
0 + r = r for some 0 and any r in R
1 * r = r for some 1 and any r in R
a * (b + c) = a*b + a*c
for all r in R, -r is also in R
Field
for all f in {F-0}, 1/f is in F
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