The implication "irreducible implies prime" is true in integral domains in which any two non-zero elements have a greatest common divisor. This is for instance the case of unique factorization …

Oct 9, 2021 · Given a polynomial over a field, what are the methods to see it is irreducible? Only two comes to my mind now. First is Eisenstein criterion. Another is that if a polynomial is …

May 13, 2011 · @okj: An irreducible representation is a map from the group to a group of matrices; under the representation (under the map), each element of the group will map to a …

Feb 1, 2019 · However, Serre is dealing with finite-dimensional complex representations of finite groups, and in that case, yes, every indecomposable representation is irreducible.

Oct 27, 2017 · Then, on the wikipedia page below, it says "an irreducible polynomial is, roughly speaking, a non-constant polynomial that cannot be factored into the product of two non …

What is an irreducible matrix? Ask Question Asked 6 years, 9 months ago Modified 6 years, 9 months ago

Why an absolutely irreducible representation is irreducible under all field extensions? Ask Question Asked 9 years, 8 months ago Modified 4 years, 7 months ago

Oct 9, 2015 · A decomposable representation is one which is not indecomposable. The relationship between the notions of irreducibility and complete reducibility is quite different …

Aug 27, 2017 · So, when you talk about a polynomial being irreducible or prime, one runs into the same sort of reason that $1$ is not prime, because the notion of irreducibility is only a useful …

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