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An imbedding theorem for separable algebras

An imbedding theorem for separable algebras

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S slash upper R"> <mml:semantics> <mml:mrow> <mml:mi>S</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mo>/</mml:mo> </mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">S/R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> be a ring extension, where <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper S"> <mml:semantics> <mml:mi>S</mml:mi> <mml:annotation encoding="application/x-tex">S</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a commutative ring. If <inline-formula content-type="math/mathml"> <mml:math …