query: Graded ring localization. Why is this function bijective?
positive_passages.docid: 106550
positive_passages.text: The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
negative_passages.docid: 32741
negative_passages.text: Idempotents in a ring without unity (rng) and no zero divisors.
negative_passages.docid: 29359
negative_passages.text: Localisation isomorphic to a quotient of polynomial ring
negative_passages.docid: 41593
negative_passages.text: Use of Bijection for computation
negative_passages.docid: 133083
negative_passages.text: Injectivity and surjectivity of a recursive function
negative_passages.docid: 155445
negative_passages.text: What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
negative_passages.docid: 15909
negative_passages.text: Bijection from $\mathbb R$ to $\mathbb {R^N}$
negative_passages.docid: 21707
negative_passages.text: Constructing a Bijective function via an injective and surjective one.
negative_passages.docid: 32443
negative_passages.text: Find the kernel of a ring homomorphism $f(x)\to f(\sqrt 2)$
negative_passages.docid: 145221
negative_passages.text: Ring isomorphism (polynomials in one variable)
negative_passages.docid: 143051
negative_passages.text: Inverting noninvertible elements in a bigger ring.
negative_passages.docid: 56020
negative_passages.text: Localization and flatness
negative_passages.docid: 1026
negative_passages.text: Ring homomorphism with $\phi(1_R) \neq1_S$
negative_passages.docid: 30714
negative_passages.text: A question on ring homomorphisms and maximal ideals.
negative_passages.docid: 64025
negative_passages.text: Ring homomorphisms from $\Bbb Q$ into a ring
negative_passages.docid: 141100
negative_passages.text: Nontrivial subring with unity different from the whole ring?
negative_passages.docid: 73689
negative_passages.text: A question about the equivalence relation on the localization of a ring.