The Structure of Quasi-Frobenius Rings
1974 ◽
Vol 26
(5)
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pp. 1141-1151
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Keyword(s):
Utilizing a matrix representation of semiperfect rings by a family of bimodules over local rings, we describe the structure of generalized quasi-Frobenius rings in two steps: a cyclic generalized quasi-Frobenius ring is a matrix ring over a cycle of Morita dualities between local rings, and an arbitrary generalized quasi-Frobenius ring is a matrix ring over a family of cyclic generalized quasi-Frobenius rings.Our results provide a complete classification of generalized quasi-Frobenius rings, modulo the classification of local rings with Morita duality, of certain bimodules over such rings, and of certain rest families of multiplication maps.
2018 ◽
Vol 168
(2)
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pp. 305-322
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Keyword(s):
2017 ◽
Vol 16
(10)
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pp. 1750197
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2016 ◽
Vol 31
(17)
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pp. 1650102
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2003 ◽
Vol 35
(6)
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pp. 1059-1076
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Keyword(s):