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• W2403245193 abstract "This paper studies similarities and differences between the classes of rings over which each simple module is injective and rings over which each simple module is $Sigma$-injective. The rings in the former class are called $V$-rings and the rings in the latter class are called $Sigma$-$V$ rings. We have obtained analogues of various well-known results about $V$-rings for $Sigma$-$V$ rings. Motivated by a conjecture of Kaplansky, Fisher asked if a prime right $V$-ring is right primitive. Although a counter-example to Kaplansky's conjecture was constructed long ago but Fisher's question is still open. In this paper we show that for a right $Sigma$-$V$ ring, the notions of prime and primitive are equivalent. Also, we show that an exchange $Sigma$-$V$ ring is left-right symmetric and moreover, it is von Neumann regular." @default.
• W2403245193 created "2016-06-24" @default.
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• W2403245193 date "2016-05-17" @default.
• W2403245193 modified "2023-09-27" @default.
• W2403245193 title "$V$-rings versus $Sigma$-$V$ Rings" @default.
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