The Integrated Software “Algebra, 7 Classes”
نویسندگان
چکیده
منابع مشابه
Algebra Homework 7
Certainly 0R ∈ A. Let a, b ∈ A. Then a ∈ An and b ∈ Am for some n,m ∈ N. Without loss of generality, assume n ≤ m. This means An ⊆ Am. So we have a, b ∈ Am. Since Am is a subring, it follows that −a ∈ Am, a + b ∈ Am, and ab ∈ Am. So also −a ∈ A, a + b ∈ A and ab ∈ A. This means A is closed under additive inverses, addition, and multiplication, so A is a subring of R. Let r ∈ R. Since An is an i...
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Proof. Let F be the field of fractions of R. By 6.2.8, we must show that R = Int(R,F). The inclusion R ⊆ Int(R,F) is immediate. Let f/g ∈ Int(R,F) and let it be written in lowest terms. Suppose to the contrary that f/g / ∈ R. Then g = q1 · · · q` with qj prime for 1 ≤ j ≤ `. We can also write f = p1 · · · pk where the pi are primes for 1 ≤ i ≤ k. Note that pi 6∼ qj for any i, j because f/g is i...
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ژورنال
عنوان ژورنال: Information Technologies in Education
سال: 2008
ISSN: 1998-6939,2306-1707
DOI: 10.14308/ite000024