All Questions
4
questions
1
vote
2
answers
255
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Reference for integral extensions of $\mathbb{Z}/p^k\mathbb{Z}$
I was looking for a reference which discusses the structure of finite integral extensions of $\mathbb{Z}/p^k\mathbb{Z}$. In particular, I am interested in understanding what the abelian group of its ...
5
votes
1
answer
217
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Intrinsic characterisation of a class of rings
This may be well known, but I was unable to find an answer browsing literature. Let us temporarily call a commutative (unital) ring $R$ an O-ring if there exists an integer $n \ge 1$, a local field of ...
3
votes
0
answers
314
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Roots of polynomials over $\mathbb{Z}/p^k\mathbb{Z}$
Over a finite field, such as $\mathbb{Z}/p\mathbb{Z}$, the number of roots of a polynomial is no larger than the degree. I'm interested in how does this generalize to $\mathbb{Z}/p^k\mathbb{Z}$.
I'm ...
4
votes
2
answers
537
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Irreducible algebraic sets via irreducible polynomials
There are many results about irreducible polynomials over finite fields:
we know a cardinality of all irreducible polynomials with given degree, we know explicit examples of irreducible polynomials, ...