Geodesic
On the Commutativity of Semi-Simple Associative Algebras
Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 485-487

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Recall that an automorphism φ of an algebra A is called regular if, for all x∊A, φ(x) = x implies x = 0. For various types of algebras it is known that the existence of a regular automorphism implies that the algebra is radical. Here, for associative algebras, we relax the restrictions on the fixed points so that all automorphisms of commutative algebras immediately satisfy the hypothesis on the fixed points. 
Stitzinger, Ernest L. On the Commutativity of Semi-Simple Associative Algebras. Canadian mathematical bulletin, Tome 20 (1977) no. 4, pp. 485-487. doi: 10.4153/CMB-1977-072-9
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     title = {On the {Commutativity} of {Semi-Simple} {Associative} {Algebras}},
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