Infinite primes and unique factorization in a principal right ideal domain
نویسندگان
چکیده
منابع مشابه
Motives and Infinite Primes
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Let R be a commutative ring throughout. Usually R will be an integral domain and even a principal ideal domain, but these assumptions will be made explicitly. Since R is commutative, there is no distinction between left, right and 2-sided ideals. In particular, for every ideal I we have a quotient ring R/I. F always denotes a field. Our goal is to prove the classification theorem for finitely-g...
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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 + ...
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KrulΓs principal ideal theorm [Krull] states that q elements in the maximal ideal of a local noetherian ring generate an ideal whose minimal components are all of height at most q. Writing R for the ring, we may consider the q elements, x19 , xq say, as coordinates of an element xeR. It is an easy observation that every homomorphism R —> R carries x to an element of the ideal generated by xi9 ,...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1969
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1969-0242879-x