July 17th, 2015, 10:00 AM  #1 
Senior Member Joined: Nov 2011 Posts: 250 Thanks: 3  ring and field
what the difference between ring to field? Is field contain ring or ring contain the field

July 17th, 2015, 10:19 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
A field is a ring where each nonzero element has a multiplicative inverse.

July 17th, 2015, 10:30 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 
"ring" and "field" are concepts in abstract algebra, not "linear algebra". (A "field" is a "ring" in which every element has a multiplicative inverse.) 
July 18th, 2015, 07:50 AM  #4 
Senior Member Joined: Apr 2014 From: Greater London, England, UK Posts: 320 Thanks: 156 Math Focus: Abstract algebra  

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