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HOW FAR IS AN ELEMENT FROM BEING PRIME?
Journal of Algebra and Its Applications, 2010Let D be an integral domain. We investigate two invariants ω(D, x) and ω(D) which measure how far an x ∈ D is from being prime and how far an atomic integral domain D is from being a UFD, respectively. We give a new characterization of number fields with class number two. We also study asymptotic versions of these two invariants.
Anderson, David F., Chapman, Scott T.
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Converse Prime Element Theorems for Arithmetical Semigroups
Mathematische Nachrichten, 2002Some growth conditions for the prime element counting function are given which imply that the zeta function of the arithmetical semigroup has a finite radius of convergence at which the zeta function attains a finite value and that simultaneously a positive proportion of the all its elements are the prime ones.
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Zero divisors and prime elements of bounded semirings
Frontiers of Mathematics in China, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wu, Tongsuo, Li, Yuanlin, Lu, Dancheng
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Filtration, asymptotic \(\sigma\)-prime divisors and superficial elements
2021Summary: Let \((A,\mathfrak{M})\) be a Noetherian local ring with infinite residue field \(A/ \mathfrak{M}\) and \(I\) be a \(\mathfrak{M}\)-primary ideal of \(A\). Let \(f = (I_n)_{n\in \mathbb{N}}\) be a good filtration on \(A\) such that \(I_1\) containing \(I\). Let \(\sigma\) be a semi-prime operation in the set of ideals of \(A\). Let \(l\geq 1\)
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Co-prime linear arrays with dipole elements
2016 IEEE Middle East Conference on Antennas and Propagation (MECAP), 2016In this paper, we study the characteristics of linear co-prime arrays (CPAs) from an array factor (AF) perspective. We start by deriving an exact expression for the array factor and compare it with the approximate formula in [1] as well as that of a uniform linear array (ULA).
Ahmed A. Al-Habob +3 more
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Finite groups with elements of prime power index
Journal of Algebra and Its Applications, 2015Let G be a finite group and let π be a set of primes. For an element x of G, let Ind G(x) denote the index of CG(x) in G. We prove that if Ind 〈a,x〉(x) is a π-number for every element a of prime power order in G, then Ind G(x) is a π-number.
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ZEROS OF CHARACTERS ON PRIME ORDER ELEMENTS
Communications in Algebra, 2001Suppose that G is a finite group, let χ be a faithful irreducible character of degree a power of p and let P be a Sylow p-subgroup of G. If χ(x) ≠ 0 for all elements of G of order p, then P is cyclic or generalized quaternion. * The research of the first author is supported by a grant of the Basque Government and by the University of the Basque Country
Alexander Moretó1*, Gabriel Navarro2†
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The number of elements of prime order
Monatshefte für Mathematik, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The prime element theorem on additive formations
Mathematische Zeitschrift, 1999Since A. Beurling 1937 published his note on the prime number theorem for generalized primes there were also many papers in which generalizations of the prime number theorem for arithmetic progressions were considered. So, in 1954 \textit{W. Forman} and \textit{H. N. Shapiro} [Commun. Pure Appl. Math.
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Enhanced prime editing systems by manipulating cellular determinants of editing outcomes
Cell, 2021Peter J Chen +2 more
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