Multivectors of rank 2 over fields and commutative rings

Journal Article · Sun Jun 30 00:00:00 EDT 2002 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM2002V193N05ABEH000652; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21205698

Kleiner, G B ^[1]

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1. Central Economics and Mathematics Institute, Russian Academy of Sciences, Moscow (Russian Federation)

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.

• OSTI ID: 21205698
• Journal Information: Sbornik. Mathematics, Vol. 193, Issue 5; Other Information: DOI: 10.1070/SM2002v193n05ABEH000652; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATION RELATIONS
INTEGRALS
VERIFICATION