A NEW NUMBER FIELD CONSTRUCTION OF THE D_4-LATTICE

J. Carmelo Interlando1, José Othon Dantas Lopes2,
Trajano Pires da Nóbrega Neto3
1Department of Mathematics and Statistics
San Diego State University
San Diego, CA 92182-7720, USA
2Department of Mathematics
Federal University of Ceará
Fortaleza, CE 60455-900, BRAZIL
3Department of Mathematics
São Paulo State University
São José do Rio Preto, SP 15054-000, BRAZIL

Abstract

A classical problem in lattice theory is to determine whether a given lattice can be realized as $\mathfrak O_K$-lattice, where $\mathfrak O_K$ is the ring of integers of some number field $K$. In this work we show that the lattice $D_4$ can be realized as an $\mathfrak O_F$-lattice for infinitely many totally real biquadratic fields $F$.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 2
Year: 2018

DOI: 10.12732/ijam.v31i2.11

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