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Isomorphic to external direct sum but internal direct sum not defined

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#linear-algebra #abstract-algebra #modules #direct-sum
84
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Proving two modules are free based on their direct sum

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#commutative-algebra #modules #direct-sum #free-modules #local-rings
102
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$\big\langle B_1\cup\cdots\cup B_p\big\rangle=\langle B_1\rangle\oplus\cdots\oplus\langle B_p\rangle$

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#linear-algebra #direct-sum
40
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Necessary and sufficient condition for a $ Z \oplus Z$ base

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#solution-verification #modules #integers #direct-sum
113
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How are submodules characterized with respect to the isomorphism of the direct sum of multiple modules?

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#ring-theory #modules #examples-counterexamples #direct-sum
187
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Let $V$ be a finite dimensional vector space and $W$ be a subspace

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#linear-algebra #vector-spaces #direct-sum
39
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Direct sum of Hilbert/Sobolev Space?

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#functional-analysis #hilbert-spaces #sobolev-spaces #direct-sum
71
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Trouble understanding direct sum in smith normal form proof

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#linear-algebra #abstract-algebra #direct-sum
39
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How are "types" defined in this module?

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#abstract-algebra #modules #direct-sum #p-groups #quotient-set
70
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Give a non-zero $R$-module $M$ such that $M \oplus M \cong M$

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#abstract-algebra #modules #direct-sum
126
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Exercise 17, Section 4.1 of Hungerford’s Algebra

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#abstract-algebra #modules #direct-sum
79
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Exercise 9, Section 4.2 of Hungerford’s Algebra

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#abstract-algebra #modules #direct-sum #free-modules
49
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Find a subspace $W$ of $P_{2}(\mathbb{R})$ such that $P_{2}(\mathbb{R})$ = $ U \oplus W$

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#linear-algebra #direct-sum
128
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Dimension of tensor product vs. dimension of direct product

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#group-theory #representation-theory #tensor-products #direct-sum #direct-product
242
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Recover direct summands in derived category?

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#algebraic-geometry #commutative-algebra #homological-algebra #direct-sum #derived-categories

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