Let O be the ring of integers of QQ[b]/(b^4 + b^3 + 2*b^2 + 2*b + 1). Then -3 has a square root in O, namely 2*b^3 + 2*b + 1. In particular, I = ((2*b^3 + 2*b + 1)^3) is a principal ideal in O of index 729. Let R be the quotient O/I. Let a = -b^3 - b - 1. Then x \diamond y = a*x + b*y defines a linear model of the ring R. Not that as a abelian group, R is isomorphic to Z/9 x Z/9 x Z/3 x Z/3. This model admits a quotient map to magma#27b44223aba3901db5370d269eb5ae77
dwrensha · 2026-06-12 15:33:48
Let O be the ring of integers of QQ[b]/(b^4 + b^3 + 2*b^2 + 2*b + 1). Then -3 has a square root in O, namely 2*b^3 + 2*b + 1. In particular, I = ((2*b^3 + 2*b + 1)^3) is a principal ideal in O of index 729. Let R be the quotient O/I. Let a = -b^3 - b - 1. Then x \diamond y = a*x + b*y defines a linear model of the ring R. Not that as a abelian group, R is isomorphic to Z/9 x Z/9 x Z/3 x Z/3. This model admits a quotient map to #27b44223aba3901db5370d269eb5ae77
b-reinke · 2026-06-12 13:05:56
Let O be the ring of integers of QQ[b]/(b^4 + b^3 + 2*b^2 + 2*b + 1). Then -3 has a square root in O, namely 2*b^3 + 2*b + 1. In particular, I = ((2*b^3 + 2*b + 1)^3) is a principal ideal in O of index 729. Let R be the quotient O/I. Let a = -b^3 - b - 1. Then x \diamond y = a*x + b*y defines a linear model of the ring R. Not that as a abelian group, R is isomorphic to Z/9 x Z/9 x Z/3 x Z/3. This model admits a quotient map to https://eq677.icarm.cloud/magma/27b44223aba3901db5370d269eb5ae77
dwrensha · 2026-06-12 15:34:02
dwrensha · 2026-06-12 15:33:48
b-reinke · 2026-06-12 13:05:56