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linear algebra - Irreducible polynomials in $\mathbb F_3 [x . . . By looking for what's missing from the $9$ monic polynomials of degree $2$, you can find the monic irreducible polynomials of degree $2$ For degree $3$, things get more complicated, but you're considering either products of three linear terms or a linear term with a degree $2$ factor
Injective vs. monic (in categories where it makes sense) Is the reason why [ monic $\implies $ injective ] true in categories of algebras (but not in other categories whose objects are sets (possibly with some structure) - let's call their objects qwertis) that for the latter categories there is no notion of "free qwerty on a set"? What are some examples (without proof)?
Monic and epic implies isomorphism in an abelian category? Split monic and epic implies iso; as does split epic and monic But monic and epic does not always imply iso The counterexample is the monoid of natural numbers, since every number considered as a morphism is both monic and epic, but there's only one number, 0, with an inverse
Finding the monic gcd of 2 polynomials [duplicate] Use Euclid’s Algorithm to find the monic gcd of (i) X^3 + 3X^2 + 4X + 2 and 2X^2 + 7X + 5 I ended up with 13 4X+13 4 = 45 13 (169 180X +169 180), but these are not monic and I don't know where I went wrong as I just followed Euclid's algorithm