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July 17th, 2015, 10:00 AM   #1
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ring and field

what the difference between ring to field? Is field contain ring or ring contain the field
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July 17th, 2015, 10:19 AM   #2
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A field is a ring where each nonzero element has a multiplicative inverse.
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July 17th, 2015, 10:30 AM   #3
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"ring" and "field" are concepts in abstract algebra, not "linear algebra".


(A "field" is a "ring" in which every element has a multiplicative inverse.)
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July 18th, 2015, 07:50 AM   #4
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Quote:
Originally Posted by Country Boy View Post
(A "field" is a "ring" in which every element has a multiplicative inverse.)
Not quite. Multiplication in a field also has to be commutative (whereas it need not be in a ring).
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