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- W2064179459 abstract "Abstract A long-standing conjecture of Faith in ring theory states that a left self-injective semi-primary ring A is necessarily a quasi-Frobenius ring. We propose a new method for approaching this conjecture, and prove it under some mild conditions; we show that if the simple A -modules are at most countably generated over a subring of the centre of A , then the conjecture holds. Also, the conjecture holds for algebras A over sufficiently large fields, i.e. if the cardinality of is larger than the dimension of the simple A -modules (or of A /Jac( A )). This effectively proves the conjecture in many situations, and we obtain several previously known results on this problem as a consequence." @default.
- W2064179459 created "2016-06-24" @default.
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- W2064179459 date "2014-12-10" @default.
- W2064179459 modified "2023-09-28" @default.
- W2064179459 title "On Semi-Primary Self-Injective Rings and Faith's Quasi-Frobenius Conjecture" @default.
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- W2064179459 doi "https://doi.org/10.1017/s0013091514000443" @default.
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