2015
DOI: 10.1080/00927872.2014.955573
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A Note on the Faith–Menal Conjecture

Abstract: The Faith-Menal conjecture is one of the three main open conjectures on QF rings. It says that every right noetherian and left FP -injective ring is QF. In this paper, it is proved that the conjecture is true if every nonzero complement left ideal of the ring R is not small (or not singular).Several known results are then obtained as corollaries.

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Cited by 4 publications
(3 citation statements)
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“…47 Shortly after its release, the IMO market in China collapsed. 48 Notwithstanding this tough approach, the Chinese government has supported the development of the underlying blockchain technology to help modernize China's financial system and to become a global leader in this cutting-edge technology, which it believes will have a similar economic and technological impact as the development of artificial intelligence. In 2019, President Xi Jinping stated that China needed to "seize the opportunities" presented by blockchain because it represents an "important breakthrough in independent innovation of core technologies."…”
Section: Cryptocurrency Laws In Chinamentioning
confidence: 99%
See 1 more Smart Citation
“…47 Shortly after its release, the IMO market in China collapsed. 48 Notwithstanding this tough approach, the Chinese government has supported the development of the underlying blockchain technology to help modernize China's financial system and to become a global leader in this cutting-edge technology, which it believes will have a similar economic and technological impact as the development of artificial intelligence. In 2019, President Xi Jinping stated that China needed to "seize the opportunities" presented by blockchain because it represents an "important breakthrough in independent innovation of core technologies."…”
Section: Cryptocurrency Laws In Chinamentioning
confidence: 99%
“…PBOC believes that blockchain technology can be developed without the use of tokens, which are believed to have been the roots of various social problems such as illegal fundraising and fraud. 51 Prohibitions on the issuance and sale of tokens are regulated in the Law of the People's Republic of China on the People's Bank of China (amended in 2003) and is administered under the supervision of the PBOC. 52 Article 20 states that "[n]o units or individuals may print or sell promissory notes as substitutes for Renminbi to circulate on the market."…”
Section: Cryptocurrency Laws In Chinamentioning
confidence: 99%
“…xvi]) which states that every right Noetherian and left FP-injective ring is quasi-Frobenius. Recently, Shen [17] has shown the Faith-Menal conjecture holds true for rings R for which every closed left ideal of the ring R is finitely generated. At present there are no known counterexamples to this statement.…”
Section: G(x)mentioning
confidence: 99%