Mohammed Sahmoudi, Abdelhakim Chillali, "Elliptic Curve on a Family of Finite Ring," WSEAS Transactions on Mathematics, vol. 18, pp. 415-422, 2019, DOI:
Mohammed Sahmoudi, Abdelhakim Chillali. Elliptic Curve on a Family of Finite Ring.
WSEAS Transactions on Mathematics. 2019;18:415-422.
WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 18, 2019
Elliptic Curve on a Family of Finite Ring
Authors: ,
Abstract: Let $$L/Q$$ be a Sextic extension, namely $$L = Q(\sqrt{d},β)$$ which is a rational quadratic over a pure cubic subfield $$K = Q(β)$$ where d is a rational square free integer and β is a root of monic irreducible polynomial of degree 3. We are interested in finding a commutative and associative ring denoted by $$\mathbb{Z}q[\sqrt{d},β]$$ using the integral closure $$O_{L}$$ of sextic extension L. Furthermore, we study the elliptic curve over this ring. Consequently, we will prove the following principal result <br>$$E_{t,s}^{q}(α,β)\cong F_{q}^{5}\bigoplus E_{α_{0},β_{0}}^{q}$$
Pages: 415-422 WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #50 DOI: *As the DOI is a unique identifier, it is already available in the pdf version.
**The DOI link will be activated in the first midst of January 2026.
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