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Algebras of homological dimension 1
V. E. Govorov
Abstract:
Augmented algebras over a field of homological dimension 1 ($\operatorname{hd}R=1$) are studied. It is proved that if $\operatorname{hd}R=1$, then the associated graded algebra $E(R)$ is free. If the filtration of the algebra $R$ defined by the powers of the augmentation ideal is separated, then the following conditions are equivalent: 1) $\operatorname{hd}R=1$, 2) $E(R)$ is free, 3) $\operatorname{w.g.dim}R=1$.
Some properties of groups of homological dimension 1 are presented.
It is proved that, in the category of graded algebras, the functor that produces homology groups carries a direct sum into a free product and a free product into a direct sum.
Bibliography: 6 titles.
Received: 07.12.1979
Citation:
V. E. Govorov, “Algebras of homological dimension 1”, Mat. Sb. (N.S.), 116(158):1(9) (1981), 111–119; Math. USSR-Sb., 44:1 (1983), 97–107
Linking options:
https://www.mathnet.ru/eng/sm2441https://doi.org/10.1070/SM1983v044n01ABEH000953 https://www.mathnet.ru/eng/sm/v158/i1/p111
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Abstract page: | 247 | Russian version PDF: | 91 | English version PDF: | 13 | References: | 38 |
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