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A Note on Weakly Symmetric Rings

Published online by Cambridge University Press:  20 November 2018

P. J. Horn
P. J. Horn*
Affiliation:
Department of Mathematics, Box 5717, Northern Arizona University, Flagstaff, Arizona 86001 U.S.A.
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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.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 531 - 533
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Fuller, K. R., On indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969), 115.Google Scholar
2. Nakayama, T., On Frobeniusean algebras I, Ann. of Math. 40 (1939), 611-633.Google Scholar