Below I will leave a list of proposed changes/point to passages in the book that, in my opinion, should be redacted.
1.
Page 14. Tautology, sentence doesn't make sense.
2.
Page 14. The article "a" is better here. (Because "the" Mathematics book doesn't exist). Or the sentence should be changed completely (e. g. using an expression "a book about Mathematics").
3.
Page 23."... whose first term and difference are COPRIME positive integers ..."
4.
Page 33. Formally speaking, statements a and b are both false, because if p=q, then gcd(p,q)=lcm(p,q)=p. To match the questions intent we should clarify that p≠q.
5.
Page 43. "... is a f̶u̶n̶c̶t̶i̶o̶n̶ homomorphism ..."
6.
Page 54. The example refutes the definition, because neither (x-sqrt(2)) nor (x+sqrt(2)) have degrees greater than one. I suggest replacing "degree more than one" with "degrees greater than zero".
7.
Page 54. I suggest replacing "more" with "greater" and "2" with "1". From fundamental theorem of algebra follows that polynomial of degree n over complex numbers has exactly n roots, so using the corollary of Bezout's Theorem, polynomial of degree 2 is not irreducible.
Below I will leave a list of proposed changes/point to passages in the book that, in my opinion, should be redacted.
1.
Page 14. Tautology, sentence doesn't make sense.
2.
Page 14. The article "a" is better here. (Because "the" Mathematics book doesn't exist). Or the sentence should be changed completely (e. g. using an expression "a book about Mathematics").
3.
Page 23."... whose first term and difference are COPRIME positive integers ..."
4.
Page 33. Formally speaking, statements a and b are both false, because if p=q, then gcd(p,q)=lcm(p,q)=p. To match the questions intent we should clarify that p≠q.
5.
Page 43. "... is a f̶u̶n̶c̶t̶i̶o̶n̶ homomorphism ..."
6.
Page 54. The example refutes the definition, because neither (x-sqrt(2)) nor (x+sqrt(2)) have degrees greater than one. I suggest replacing "degree more than one" with "degrees greater than zero".
7.
Page 54. I suggest replacing "more" with "greater" and "2" with "1". From fundamental theorem of algebra follows that polynomial of degree n over complex numbers has exactly n roots, so using the corollary of Bezout's Theorem, polynomial of degree 2 is not irreducible.