Do isomorphic structural matrix rings have isomorphic graphs?
Do isomorphic structural matrix rings have isomorphic graphs?
We first provide an example of a ring <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper R"> <mml:semantics> <mml:mi>R</mml:mi> <mml:annotation encoding="application/x-tex">R</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that all possible <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 times 2"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> <mml:annotation encoding="application/x-tex">2\times 2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> structural matrix rings over <inline-formula content-type="math/mathml"> …