Geodesic
A Note on Weakly Symmetric Rings
Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 531-533

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T. Nakayama showed in [2, Theorem 13] that symmetric algebras have the property that the left and right annihilators of their two-sided ideals are equal. He also gave examples [2, p. 630] to show that QF algebras with this property are not necessarily symmetric, and that weakly symmetric algebras need not have this property. 
Horn, P. J. A Note on Weakly Symmetric Rings. Canadian mathematical bulletin, Tome 17 (1974) no. 4, pp. 531-533. doi: 10.4153/CMB-1974-094-x
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     title = {A {Note} on {Weakly} {Symmetric} {Rings}},
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