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How to prove a sum formula about powers of 2 and 3?

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#combinatorics #summation #induction #exact-sequence
111
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Exact sequence in cohomology while studying orientability of Alexandrov spaces

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#algebraic-topology #exact-sequence #metric-geometry
93
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Exact sequence of groups: proof of injectivity

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#abstract-algebra #group-theory #group-homomorphism #exact-sequence
4.3k
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Does every short exact sequence split?

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#abstract-algebra #proof-verification #algebraic-topology #homological-algebra #exact-sequence
33
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Can we deduce the exactness of the pervious modules sequence if the localized exact modules sequence is exact?

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#homological-algebra #exact-sequence #flatness
1.8k
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What is the intuition behind short exact sequences of groups; in particular, what is the intuition behind group extensions?

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#group-theory #soft-question #category-theory #intuition #exact-sequence
58
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What do $0$ and $1$ mean in a extension (exact sequence) of group?

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#group-theory #homological-algebra #exact-sequence
132
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Certain exact functor on the Grothendieck group of a module category

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#modules #exact-sequence #abelian-categories #algebraic-k-theory #artinian
397
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Every short exact sequence with a simple module splits

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#abstract-algebra #ring-theory #modules #exact-sequence
202
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Betti Numbers' inequality and Mayer-Vietoris sequence

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#algebraic-topology #exact-sequence #betti-numbers
189
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Homotopy between unitary element and identity elements, Operator Theory

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#algebraic-topology #operator-theory #operator-algebras #exact-sequence
68
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methods for computing cohomology from data of an exact sequence

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#category-theory #sheaf-theory #exact-sequence #derived-categories
165
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Short exact sequence of algebras implies bimodule structure

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#abstract-algebra #exact-sequence #bimodules
206
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Projective modules in long exact sequences

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#homological-algebra #exact-sequence #projective-module #free-modules
395
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Baer sum, pushback of pushout and pushout of pullback

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#abstract-algebra #commutative-algebra #modules #exact-sequence

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