Ideal Factorization
نویسنده
چکیده
which is impossible since the right side is even. The proof that (2, 1− √ −5) 6= (1) is similar. For another proof, complex conjugation is an operation on ideals, a 7→ a := {α : α ∈ a} which respects addition and multiplication of ideals, and (α, β) = (α, β). In particular, the conjugate of (2, 1 + √ −5) is (2, 1− √ −5), so if (2, 1 + √ −5) = (1) then (2, 1− √ −5) = (1), so the product (2, 1 + √ −5)(2, 1− √ −5) = (2) is (1)(1) = (1). But (2) 6= (1) since 2 is not a unit in Z[ √ −5].
منابع مشابه
From torsion theories to closure operators and factorization systems
Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].
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