20221224, 22:42  #1 
"David Kirkby"
Jan 2021
Althorne, Essex, UK
2·229 Posts 
Galois Fields
Someone asked the following on an amateur radio forum. I would be interested in any answers, that I can point him to. He is a very switchedon engineer, but does not have any number theory books.
A simple question none of the mathematical texts I've tried to study have actually made clear : Is Modulo arithmetic under MOD(any prime number) a Galois Field? Always? If not, what's different? addition and multiplication work in the field, ie (a + b) MOD p and a.b MOD p always result in complete use of the set of numbers 0 to p1 so I think that qualifies. Why do the books not appear to explicitly say so? The texts discuss module prime arithmetic being a 'field', then usually move to polynomials and Galois Fields in the next page or two. And I'm missing something in the intermediate jump. Is it assumed and I'm being too pedantic? Last fiddled with by drkirkby on 20221224 at 22:48 
20221224, 23:50  #2 
Apr 2020
13·79 Posts 
A Galois field is just another name for a finite field. So yes, arithmetic modulo any prime is a Galois field  though not every Galois field is of this type.

20221225, 06:45  #3 
"David Kirkby"
Jan 2021
Althorne, Essex, UK
2×229 Posts 

Thread Tools  
Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Fields Medals 2022  charybdis  Math  4  20230602 16:51 
Galois insertion  karenilsen  Homework Help  1  20220112 10:29 
Questions about Number Fields  Raman  Miscellaneous Math  5  20130612 13:54 
parigp and trigonometry in Galois fields  __HRB__  Math  1  20100612 20:09 
On the basis of finite fields  meng_luckywolf  Math  6  20071213 04:21 