African Journal of Mathematics and Computer Science Research
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Article Number - 7B9E0E966705


Vol.10(5), pp. 32-37 , November 2017
https://doi.org/10.5897/AJMCSR2015.0625
ISSN: 2006-9731


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Adams completion and symmetric algebra



M. Routaray
  • M. Routaray
  • Department of Mathematics, National Institute of Technology ROURKELA - 769008 India.
  • Google Scholar
A. Behera
  • A. Behera
  • Department of Mathematics, National Institute of Technology ROURKELA - 769008 India.
  • Google Scholar







 Received: 02 August 2015  Accepted: 22 September 2015  Published: 30 November 2017

Copyright © 2017 Author(s) retain the copyright of this article.
This article is published under the terms of the Creative Commons Attribution License 4.0


Deleanu, Frei and Hilton have developed the notion of generalized Adams completion in a categorical context. In this paper, the symmetric algebra of a given algebra is shown to be the Adams completion of the algebra by considering a suitable set of morphisms in a suitable category.

Key words: Category of fraction, calculus of left fraction, symmetric algebra, tensor algebra, Adams completion.

Adams JF (1973). Idempotent functors in homotopy theory, Manifolds, Conf. Univ. of Tokyo Press, Tokyo.

 

Adams JF (1975). Localization and completion, Lecture Notes in Mathematics, Univ. of Chicago.

 
 

Behera A, Nanda S (1987). Mod- Postnikov approximation of a 1-connected space, Canad. J. Math. 39(3):527- 543.
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Deleanu A, Frei A, Hilton P (1974). Generalized Adams completions, Cahiers de et Geom. Diff. 15(1):61-82.

 
 

Deleanu A (1975). Existence of the Adams completion for objects of complete categories. J. Pure Appl. Algebra. 6(1):31-9.
Crossref

 
 

Grinberg D (2013). A few classical results on tensor, symmetric and exterior powers. 

 
 

Murfet D (2006). Tensor, Exterior and symmetric algebra. 

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Schubert H (1972). Categories, Springer Verlag, New York.
Crossref

 

 


APA Routaray, M., & Behera, A. (2017). Adams completion and symmetric algebra. African Journal of Mathematics and Computer Science Research, 10(5), 32-37.
Chicago M. Routaray and A. Behera. "Adams completion and symmetric algebra." African Journal of Mathematics and Computer Science Research 10, no. 5 (2017): 32-37.
MLA M. Routaray and A. Behera. "Adams completion and symmetric algebra." African Journal of Mathematics and Computer Science Research 10.5 (2017): 32-37.
   
DOI https://doi.org/10.5897/AJMCSR2015.0625
URL http://academicjournals.org/journal/AJMCSR/article-abstract/7B9E0E966705

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