query: Hartshorne Remark II.5.16.1
positive_passages.docid: 156005
positive_passages.text: Pullback of locally free sheaves is locally free
negative_passages.docid: 62603
negative_passages.text: Characterizations of the $p$-Prüfer group
negative_passages.docid: 132653
negative_passages.text: How to show that $\mathfrak{sl}_n(\mathbb{R})$ and $\mathfrak{sl}_n(\mathbb{C})$ are simple?
negative_passages.docid: 119758
negative_passages.text: On the order of elements of $\mathrm{GL}(2,q)$.
negative_passages.docid: 55257
negative_passages.text: Egoroff's theorem in Royden Fitzpatrick (comparison with lemma 10)
negative_passages.docid: 117131
negative_passages.text: Canonical Isomorphism Between $\mathbf{V}$ and $(\mathbf{V}^*)^*$
negative_passages.docid: 89659
negative_passages.text: $H_1 ,H_2 \unlhd \, G$ with $H_1 \cap H_2 = \{1_G\} $. Prove every two elements in $H_1, H_2$ commute
negative_passages.docid: 141067
negative_passages.text: Theorem 20 Hoffman Kunze Linear Algebra book Section 3.6
negative_passages.docid: 15686
negative_passages.text: Product of a Lie ideal with a subalgebra
negative_passages.docid: 20407
negative_passages.text: Proof of Wolstenholme's theorem
negative_passages.docid: 34183
negative_passages.text: An equivalent condition with $\{0\}$ being the only nilpotent ideal
negative_passages.docid: 99217
negative_passages.text: Hartshorne's Exercise II.4.5(c). A third time.
negative_passages.docid: 12104
negative_passages.text: How to prove this result involving the quotient maps and connectedness?
negative_passages.docid: 38571
negative_passages.text: Localization of a total quotient ring of a reduced ring
negative_passages.docid: 156611
negative_passages.text: Hartshorne Problem 1.2.14 on Segre Embedding
negative_passages.docid: 47086
negative_passages.text: Quotient rings and free modules
negative_passages.docid: 80788
negative_passages.text: Cech Cohomology Hartshorne III 4.4