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In this paper, we provide a formula for the vector space dimension of the ring $\mathbb{F}_2[x,y,z]/(x^{d_1}, y^{d_2},z^{d_3}, x+y+z)$ over $\mathbb{F}_2$ when $d_1,d_2,d_3$ all lie between successive powers of $2$. For general $d_1,d_2,d_3$, we prov
Externí odkaz:
http://arxiv.org/abs/2306.16574
Polynomial quotient rings are fundamental objects in commutative algebra. They play a big role in many areas of study, ranging from the applied sciences (cryptography, coding theory) to higher-level mathematics (algebraic geometry, field theory). Giv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c56fc2ef57b11f1f8d3e568122551d48