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15
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Is there a counterexample for the claim: if $A \oplus B\cong A\oplus C$ then $B\cong C$?

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#abstract-algebra #modules #finitely-generated
255
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Is $m$ a projective $A$-module?

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#commutative-algebra #modules #projective-module
58
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One-dimensional submodules of $\mathbb{C}^4$; direct sum of submodules.

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#modules #representation-theory #direct-sum
50
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Are there terminologies distinguishing these two ranks?

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#abstract-algebra #terminology #modules #definition #finitely-generated
1.6k
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Relation between two definitions of primary modules

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#commutative-algebra #modules
352
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Zorn's Lemma Application for Finding Maximal Submodule?

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#abstract-algebra #modules
821
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Simple modules over R isomorphic to R/I

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#linear-algebra #field-theory #modules #ideals
39
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Is there another terminology to designate this?

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#abstract-algebra #terminology #modules
99
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Submodules $H$ satisfying: "if $ax \in H$ for some non-zero scalar $a$, then $x \in H$."

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#commutative-algebra #terminology #modules
272
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Injective homomorphism on tensor product

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#modules #tensor-products
81
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If $I$ and $J$ are ideals of an $R$-algebra $A=I+J$ then $I\oplus J\simeq A\oplus (I\cap J)$?

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#abstract-algebra #modules
43
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Homomorphisms inbetween factor modules

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#linear-algebra #modules #transformation #gcd-and-lcm
367
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The annihilator induces a module

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#linear-algebra #ring-theory #modules #ideals
6.2k
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$||x-2|-3| >1$, then $x$ belongs to which interval

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#inequality #modules
1.6k
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Why is a submodule of a free module over a PID is free?

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#abstract-algebra #modules #principal-ideal-domains

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