Ramification in quartic cyclic number fields $K$ generated by $x^4+px^2+p$ [PDF]
Mathematica Bohemica, 2021 If $K$ is the splitting field of the polynomial $f(x)=x^4+px^2+p$ and $p$ is a rational prime of the form $4+n^2$, we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q{\mathcal O}_K$, where $q$ is a positive rational
Julio Pérez-Hernández +1 more
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On Indices of Septic Number Fields Defined by Trinomials x7 + ax + b
Mathematics, 2023 Let K be a septic number field generated by a root, α, of an irreducible trinomial, x7+ax+b∈Z[x]. In this paper, for every prime integer, p, we calculate νp(i(K)); the highest power of p dividing the index, i(K), of the number field, K. In particular, we
Lhoussain El Fadil
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Variations of primeness and factorization of ideals in Leavitt path algebras [PDF]
Communications in Algebra, 2021 In this paper we describe three different variations of prime ideals: strongly irreducible ideals, strongly prime ideals and insulated prime ideals in the context of Leavitt path algebras. We give necessary and sufficient conditions under which a proper ideal of a Leavitt path algebra $L$ is a product as well as an intersection of finitely many of ...
Aljojani, Sarah +3 more
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Ideals as generalized prime ideal factorization of submodules
, 2023 For a submodule $N$ of an $R$-module $M$, a unique product of prime ideals in $R$ is assigned, which is called the generalized prime ideal factorization of $N$ in $M$, and denoted as ${\mathcal{P}}_M(N)$. But for a product of prime ideals ${{\mathfrak{p}_1} \cdots {\mathfrak{p}_{n}}}$ in $R$ and an $R$-module $M$, there may not exist a submodule $N$ in
Thulasi, K. R. +2 more
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Examples of non-Noetherian domains inside power series rings [PDF]
, 2014 Let R* be an ideal-adic completion of a Noetherian integral domain R and let L be a subfield of the total quotient ring of R* such that L contains R. Let A denote the intersection of L with R*.
Heinzer, William +2 more
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On monogenity of certain pure number fields of degrees $2^r\cdot3^k\cdot7^s$ [PDF]
Mathematica BohemicaLet $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a complex root $\alpha$ of a monic irreducible polynomial $ F(x) = x^{2^r\cdot3^k\cdot7^s} -m \in\bb{Z}[x]$, where $r$, $k$, $s$ are three positive natural integers.
Hamid Ben Yakkou, Jalal Didi
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Factorizations of Elements in Noncommutative Rings: A Survey [PDF]
, 2016 We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations.
A Geroldinger +56 more
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Submodules having the same generalized prime ideal factorization
, 2023 In our recent work, we introduced a generalization of the prime ideal factorization in Dedekind domains for submodules of finitely generated modules over Noetherian rings. In this article, we find conditions for the intersection of two submodules to have the same factorization as the submodules. We also find the relation between the factorizations of a
Thulasi, K. R. +2 more
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Maximal chains of prime ideals of different lengths in unique factorization domains [PDF]
Rocky Mountain Journal of Mathematics, 2019 20 pages, 3 figures.
Loepp, Susan, Semendinger, Alex
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On common index divisors and monogenity of septic number fields defined by trinomials of type $x^7+ax^5+b$ [PDF]
Mathematica BohemicaLet $K $ be a septic number field generated by a root $\theta$ of an irreducible polynomial $ F(x)= x^7+ax^5+b \in\mathbb Z[x]$. In this paper, we explicitly characterize the index $i(K)$ of $K$.
Hamid Ben Yakkou
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