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by ecesena
5185 days ago
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A small summary: 1. Z/pZ is a field if and only if p is prime. 2. for every p prime and n>=1 there exists a unique (up to isomorphism) field, called Galois field (see any book of algebra for the proof). 3. you can build a field of p^n elements for every p and n>1, using polynomials over Z/pZ mod an irreducible polynomial of degree n, e.g. (see link) you can build F_{2^8} as polynomials with coefficients in Z_2 (i.e. bits) mod x^8 + x^4 + x^3 + x + 1. If you chose another irreducible polynomial, e.g. x^8 + x^4 + x^3 + x^2 + 1, then you get another representation of a field of 256 elements, but "structurally" they are the same (this should "explain" the expression "up to isomorphism") |
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If you read the post you don't need the summary because you just read the post, which btw, ends with a summary.
If you didn't read the post yet and know nothing about the field, your summary won't teach them anything, and more importantly it won't tell them anything about the post. It won't tell them it's a great, catchy, read, it might only scare them away with hard, math stuff.
If you didn't read the post yet and know a lot about the field, your summary won't teach them anything because there's nothing to teach. All it can do is create a false impression about what the articles is about, but looking at your other posts in this thread I see this is your intention anyway.