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ABSTRACT
A base of the universal multiplicative envelope for the free Malcev superalgebra on one odd generator is constructed. Some corollaries for central skew-symmetric elements in free Malcev and free alternative algebras are obtained. In particular, the Malcev Grassmann algebra is constructed.
Mathematics Subject Classification:
ACKNOWLEDGMENTS
Ivan Shestakov is partially supported by CNPq, grant 304633/03-8. Natalia Zhukavets is partially supported by the Institutional Grant MSM 6840770010, Czech Republic, and by FAPESP, grant 03/01237-2.
Notes
Communicated by B. Allison.
1Note that on the preliminary stage of the proof of this proposition, the use of the computer program “Malcev” (Buchnev et al., Citation1998) was very useful.