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This article is cited in 8 scientific papers (total in 8 papers)
On the representation of finite rings by matrices over commutative rings
Yu. N. Mal'tsev
Abstract:
The author constructs an infinite series of finite rings $B$, $B^{(m)}$, $m\geqslant2$, which are not embeddable in rings of matrices over commutative rings, and describes their bases of identities and critical rings of the varieties they generate. He shows that finite rings from the ring varieties $\operatorname{var}B$, $\operatorname{var}B^{(m)}$, $m\geqslant2$, $m=(p-1)t+1$, are either representable by matrices over commutative rings or generate the respective varieties. Under a supplementary restriction on a variety $\mathfrak M$ with exponent $p^k$ it is shown that every finite ring from $\mathfrak M$ is representable by matrices over a commutative ring if and only if $\mathfrak M$ does not contain any of the rings $B$, $B^{(m)}$, $m\geqslant2$.
Bibliography: 14 titles.
Received: 23.07.1984
Citation:
Yu. N. Mal'tsev, “On the representation of finite rings by matrices over commutative rings”, Mat. Sb. (N.S.), 128(170):3(11) (1985), 383–402; Math. USSR-Sb., 56:2 (1987), 379–402
Linking options:
https://www.mathnet.ru/eng/sm2166https://doi.org/10.1070/SM1987v056n02ABEH003042 https://www.mathnet.ru/eng/sm/v170/i3/p383
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Abstract page: | 352 | Russian version PDF: | 110 | English version PDF: | 10 | References: | 40 |
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