Geodesic
On finite strongly critical rings
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1722-1729 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the present paper, some properties of strongly critical rings are investigated. It is proved that every simple finite ring and each critical ring of order $ p ^ 2 $ ($ p $ is a prime) are strongly critical. There is an example of critical ring of order 8 which is not strongly critical. It is also proved that if $ R $ is a finite ring and $ M_n (R) $ is a strongly critical ring, then $ R $ is a strongly critical ring. For rings with unity, it is proved that: 1) if $ R $ is a finite ring, $ R / J (R) = M_n (GF (q)) $ and $ J (R) $ is a strongly critical ring, then $ R $ is a strongly critical ring; 2) $R$ is strongly critical ring iff $M_n(R)$ is a strongly critical ring (for any $n\geq 1$).
Keywords: finite ring, critical ring, strongly critical ring. 
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     author = {Yu. N. Maltsev and E. V. Zhuravlev},
     title = {On finite strongly critical rings},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1722--1729},
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     volume = {17},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a38/}
}
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Yu. N. Maltsev; E. V. Zhuravlev. On finite strongly critical rings. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1722-1729. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a38/

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