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Sbornik: Mathematics, 2002, Volume 193, Issue 5, Pages 709–725
DOI: https://doi.org/10.1070/SM2002v193n05ABEH000652 (Mi sm652) 		 
Multivectors of rank 2 over fields and commutative rings

G. B. Kleiner

Central Economics and Mathematics Institute, RAS
English version PDF (249 kB) Russian version article
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DOI: https://doi.org/10.1070/SM2002v193n05ABEH000652
Abstract: In this paper the following question is studied: when can a homogeneous element of a Grassmann algebra be represented as the sum of two decomposable elements? For an exterior algebra over a field necessary and sufficient conditions of such a representation are obtained, over an arbitrary integral domain several necessary conditions, and over Krull rings also several sufficient conditions. In particular, it is established that the only rings such that the verification of 2-decomposability is carried out in the same way as over fields are the fields, that is, there are no “2-Plucker” rings.
Received: 08.11.2000
Bibliographic databases:
UDC: 512.552
MSC: Primary 15A75; Secondary 13C10
Language: English
Original paper language: Russian
Citation: G. B. Kleiner, “Multivectors of rank 2 over fields and commutative rings”, Sb. Math., 193:5 (2002), 709–725
Citation in format AMSBIB
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\by G.~B.~Kleiner
\paper Multivectors of rank 2 over fields and commutative rings
\jour Sb. Math.
\yr 2002
\vol 193
\issue 5
\pages 709--725
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    Russian version PDF:194
    English version PDF:9
    References:69
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