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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Quaternion algebras over $k[[u,v]]$
Let $R=k[[u,v]]$ be a power series ring over algebraically closed
field of characteristic zero. The quaternionic $R$-algebra is
$A=R\langle x,y\rangle/I$, where $I=(x^2-a, y^2-b, xy+yx-2c)$ and $a,b,c …