8 Answered Questions for the topic Abstract Algebra

Abstract Algebra

11/06/20

(abstract algebra)Prove that every matrix in SO3(R) has an eigenvalue λ = 1. Is it true for SO2(R)?
Prove that every matrix in SO3(R) has an eigenvalue λ = 1. Is it true for SO2(R)?
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Abstract Algebra

06/23/20

Let (G, *) be a group. Prove that the map π : G → G defined by π(g) = g * g is a homomoprhism if and only if G is abelian
Let (G, *) be a group. Prove that the map π : G → G defined by π(g) = g * g is ahomomoprhism if and only if G is abelian
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Abstract Algebra Algebra

06/19/20

Abstract algebra

Prove that if R is a ring and I ▹ R, then R[x]/I [x] ≃ (R/I )[x] for any indeterminate x.
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05/02/19

Must eigenvalues be numbers?
This is more a conceptual question than any other kind. As far as I know, one can define matrices over arbitrary fields, and so do linear algebra in different settings than in the typical... more
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03/27/19

Help me focus my study for the GRE math subject exam?
I'm preparing for the GRE Math Subject test, but I'm at a bit of a disadvantage, having never taken an algebra class or a probability class. Obviously I'm not going to learn a semester of abstract... more
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Abstract Algebra Gre Gre Exam

03/19/19

A question from GRE math sub 9367, problem 59?
Two subgroups H and K of a group G have orders 12 and 30, respectively. Which of the following could NOT be the order of the subgroup of G generated by H and K? A. 30 B. 60 C. 120 D. 360 E.... more
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03/18/19

Irreducible but not prime element?
>I am looking for a ring element which is irreducible but not prime. So necessarily the ring can't be a PID. My idea was to consider $R=K[x,y]$ and $x+y\\in R$. This is irreducible because in... more
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Abstract Algebra Logic Proofs Mathematics

12/08/18

How do I prove this statement using the axioms of integer arithmetic: If a < 0, b > 0, then ab < 0?
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