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)?

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

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.

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...
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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...
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#### 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....
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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...
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