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Mathematics of the USSR-Sbornik, 1983, Volume 44, Issue 1, Pages 97–107
DOI: https://doi.org/10.1070/SM1983v044n01ABEH000953
(Mi sm2441)
 

Algebras of homological dimension 1

V. E. Govorov
References:
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
Russian version:
Matematicheskii Sbornik. Novaya Seriya, 1981, Volume 116(158), Number 1(9), Pages 111–119
Bibliographic databases:
UDC: 513.836
MSC: 16A60
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{Gov81}
\by V.~E.~Govorov
\paper Algebras of homological dimension~1
\jour Mat. Sb. (N.S.)
\yr 1981
\vol 116(158)
\issue 1(9)
\pages 111--119
\mathnet{http://mi.mathnet.ru/sm2441}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=632491}
\zmath{https://zbmath.org/?q=an:0497.16012|0483.16025}
\transl
\jour Math. USSR-Sb.
\yr 1983
\vol 44
\issue 1
\pages 97--107
\crossref{https://doi.org/10.1070/SM1983v044n01ABEH000953}
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  • 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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