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Apr
15
comment every finitely generated vector space has a basis. Question about the proof
Yes, proceeding by induction means exactly that, keep discarding elements until you get an independent set of generators.
Apr
15
revised every finitely generated vector space has a basis. Question about the proof
Fixed brackets
Apr
15
answered every finitely generated vector space has a basis. Question about the proof
Apr
15
comment Why $K = (X_1, X_2, …)$, the ideal generated by $X_1, X_2, …$ not finitely generated as a R-module?
@user136266,$X_t$ is an indeterminate.
Apr
14
revised Definition of a Finite Normal Extension
added 331 characters in body
Apr
14
answered Definition of a Finite Normal Extension
Apr
14
revised find the minimal polynomial over $\mathbb{Q}$ of the algebraic number $\mathbb{(1+\sqrt{5})/2}$
added 6 characters in body; edited title
Apr
14
comment Multiple Group Representations using Cayley's Thm
I believe what you are saying is correct.
Apr
14
answered Multiple Group Representations using Cayley's Thm
Apr
14
revised Why $K = (X_1, X_2, …)$, the ideal generated by $X_1, X_2, …$ not finitely generated as a R-module?
added 4 characters in body
Apr
14
answered Why $K = (X_1, X_2, …)$, the ideal generated by $X_1, X_2, …$ not finitely generated as a R-module?
Apr
14
revised Why $K = (X_1, X_2, …)$, the ideal generated by $X_1, X_2, …$ not finitely generated as a R-module?
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Apr
14
comment Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
So, as advised also by @egreg, try to find three sets $A, B, C$ which satisfy $A \cap B \cap C = \emptyset$ but not (any of) the $A \cap B = A \cap C = B \cap C = \emptyset$. You don't have to look far, you can choose $A, B, C \subset \{1, 2, 3\}$.
Apr
14
comment Show that $A∩B∩C= ∅$ is only true when $A∩B = ∅, A∩C = ∅$ or $B∩C = ∅$ or show a counterexample.
I believe you are confused about the question itself, which I believe to be the following: Suppose $A, B, C$ are three sets, such that $A \cap B \cap C = \emptyset$. Is it true that $A \cap B = A \cap C = B \cap C = \emptyset$?
Apr
14
comment Showing a linear combination of matrices is nilpotent for any constants
Thanks a lot @abel
Apr
14
revised Showing a linear combination of matrices is nilpotent for any constants
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Apr
14
revised Showing a linear combination of matrices is nilpotent for any constants
deleted 382 characters in body
Apr
14
revised Showing a linear combination of matrices is nilpotent for any constants
added 6 characters in body
Apr
13
comment Showing a companion matrix is normal
$\overline{a_{0} \bar{a_{1}}} = \bar{a_{0}} a_{1}$, and you're done. This is because $\bar{\bar{a}} = a$, and $\overline{a b} = \bar{a} \bar{b}$.
Apr
13
revised Exercise in group action blocks
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