Generalized quaternion algebras
Copyright policy )Generalized quaternion algebras
Es sei \(A\) ein kommutativer Ring, in dem 2 invertierbar ist. Zu invertierbaren Elementen \(a,b\in A\) sei \(Q=(a,b/A)\) die verallgemeinerte Quaternionenalgebra. Der Verf. zeigt, daß \(Q\) genau dann rechtsdistributiv ist, wenn \(A\) distributiv und die quadratische Form \(x^2-ay^2-bz^2\) nullteilig modulo jedem maximalen Ideal \(M\) von \(A\) ist. Ist \(Q=(-1,-1/A)\) rechtsdistributiv, so ist \(1/2\in A\).
- Energy Institute United Kingdom
right distributive rings, Complete distributivity, generalized quaternion algebras, Finite rings and finite-dimensional associative algebras, Finite-dimensional division rings, Forms and linear algebraic groups, Ideals in associative algebras, quadratic forms
right distributive rings, Complete distributivity, generalized quaternion algebras, Finite rings and finite-dimensional associative algebras, Finite-dimensional division rings, Forms and linear algebraic groups, Ideals in associative algebras, quadratic forms
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