anonymous
  • anonymous
definition of field?
Algebra
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
sloppycanada
  • sloppycanada
Field? Like a soccer field?
FaireGaming
  • FaireGaming
In abstract algebra, a field is a nonzero commutative division ring, or equivalently a ring whose nonzero elements form an abelian group under multiplication.
sloppycanada
  • sloppycanada
https://en.wikipedia.org/wiki/Field_(mathematics)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
what is the ring?
FaireGaming
  • FaireGaming
the (Mathematics) ring on the link?
zzr0ck3r
  • zzr0ck3r
a ring is a group with another operation that is associative and has identity and the later operation distributes over the group operation
zzr0ck3r
  • zzr0ck3r
example. The real numbers abelian group with respect to addition: a+0=a=0+a for all a and 0 is real a+b is a real number for all a,b a+-a=0 for all real a a+b=b+a multiplication a(bc)=(ac)b 1 is a real number 1*a=a*1=a for all a distributes a(b+c) = ab+ac for all ab
zzr0ck3r
  • zzr0ck3r
the first comment I left should say "abelian group"
thomas5267
  • thomas5267
Put it simply, ring is something with two operations, addition and multiplication. Ring addition follows the same properties of real number addition, namely, - (a + b) + c = a + (b + c) for all a, b, c in R (+ is associative). - a + b = b + a for all a, b in R (+ is commutative). - There is an element 0 in R such that a + 0 = a for all a in R (0 is the additive identity). - For each a in R there exists −a in R such that a + (−a) = 0 (−a is the additive inverse of a). - a + b in R for all a, b in R. (Closure) However, the multiplication is different in a ring compared to the real numbers. The multiplication in ring satisfies the following properties. - (a ⋅ b) ⋅ c = a ⋅ (b ⋅ c) for all a, b, c in R (⋅ is associative). - There is an element 1 in R such that a ⋅ 1 = a and 1 ⋅ a = a for all a in R (1 is the multiplicative identity). - a ⋅ b in R for all a, b in R. (Closure) However, there is usually no multiplicative inverse for elements in ring, that is you cannot divide one element by another element in a ring. Furthermore, ring multiplication need not be commutative (a ⋅ b != b ⋅ a) and usually isn't.
thomas5267
  • thomas5267
A field is a ring satisfying addition properties. A field is something like real number (or should I say real number is a field). The addition axioms of a ring are unchanged for a field. However, the following multiplication axioms are added. - For each a in R there exists b in R such that a ⋅ b = b ⋅ a = 1 (b is the multiplicative inverse of a). - a ⋅ b = b ⋅ a for all a, b in R (⋅ is commutative). Since there exist a multiplicative inverse for each element in a field, you can divide one element by another in a field.

Looking for something else?

Not the answer you are looking for? Search for more explanations.