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- W3206216627 abstract "Let $Tr$ denote the trace $mathbb{Z}$-module homomorphism defined on the ring $mathcal{O}_{L} $ of the integers of a number field $L.$ We show that $Tr(mathcal{O}_{L})varsubsetneq mathbb{Z}$ if and only if there is a prime factor $p$ of the degree of $L$ such that if $wp _{1}^{e_{1}}...wp _{s}^{e_{s}}$ is the prime factorization of the ideal $pmathcal{O}_{L}$ in $mathcal{O}_{L},$ then $p$ divides all powers $e_{1},...,e_{s}.$ Also, we prove that the equality $Tr(mathcal{O}_{L})=mathbb{Z}$ holds when $L$ is the compositum of certain number fields." @default.
- W3206216627 created "2021-10-25" @default.
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- W3206216627 date "2021-10-13" @default.
- W3206216627 modified "2023-09-27" @default.
- W3206216627 title "On the trace of the integers of a number field" @default.
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- W3206216627 hasPublicationYear "2021" @default.
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