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ZINBIEL ALGEBRAS AND COMMUTATIVE ALGEBRAS WITH DIVIDED POWERS

Published online by Cambridge University Press:  25 November 2009

IOANNIS DOKAS
IOANNIS DOKAS*
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, CY-1678 Nicosia, Cyprus e-mail: dokas@ucy.ac.cy
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Abstract

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In this paper, we prove that any Zinbiel algebra can be endowed with the structure of commutative algebra with divided powers. We introduce the notion of universal enveloping Zinbiel algebra of a commutative algebra with divided powers algebras. We prove that the free divided powers algebra on a free module M, is the divided powers sub-algebra generated by M, of the divided powers algebra induced by the free Zinbiel algebra on M. Finally, we construct a basis for the enveloping Zinbiel algebra.

Keywords

17A3217A0113A99
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 303 - 313
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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