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a class of number fields without odd rational prime index divisors
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نویسنده
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didi jalal ,sahmoudi mohammed ,chillali abdelhakim
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منبع
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journal of algebra and related topics - 2025 - دوره : 13 - شماره : 2 - صفحه:149 -163
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چکیده
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in this work, for every number field k generated by a root of a monic irreducible trinomial f(x) = x^{7} + a.x^{6} + b in mathbb{z}[x], we show that no odd rational prime p divides the index i(k), and we give the necessary and sufficient conditions on a, b such that 2 divides i(k). specifically, we provide adequate requirements for k to be non-monogenic. finally, several computational examples are used to illustrate our conclusions.
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کلیدواژه
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monogeneity ,newton polygon ,prime ideal factorization ,dedekind ,common index divisor ,theorem of ore
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آدرس
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university of sidi mohamed ben abdellah, department of mathematics, lsi laboratory, morocco, university of moulay ismail, department of mathematics, morocco, university of sidi mohamed ben abdellah, department of mathematics, lsi laboratory, morocco
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پست الکترونیکی
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abdelhakim.chillali@usmba.ac.ma
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Authors
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