African Journal of
Mathematics and Computer Science Research

  • Abbreviation: Afr. J. Math. Comput. Sci. Res.
  • Language: English
  • ISSN: 2006-9731
  • DOI: 10.5897/AJMCSR
  • Start Year: 2008
  • Published Articles: 262

Review

Adams completion and symmetric algebra

M. Routaray
  • M. Routaray
  • Department of Mathematics, National Institute of Technology ROURKELA - 769008 India.
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A. Behera
  • A. Behera
  • Department of Mathematics, National Institute of Technology ROURKELA - 769008 India.
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  •  Received: 02 August 2015
  •  Accepted: 22 September 2015
  •  Published: 30 November 2017

 ABSTRACT

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.


 INTRODUCTION

The notion of generalized completion (Adams completion) arose from a categorical completion process suggested by Adams (1973, 1975). Originally this was considered for admissible categories and generalized homology (or cohomology) theories. Subsequently, this notion has been considered in a more general framework by Deleanu et al. (1974) where an arbitrary category and an arbitrary set of morphisms of the category are considered; moreover they have also suggested the dual notion, namely the completion (Adams completion) of an object in a category.
 
 
 
 
 
 
 
 
 
 
 
 
 
 


 SYMMETRIC ALGEBRA

Symmetric algebra


 RESULT


 CONFLICT OF INTERESTS

The authors have not declared any conflict of interests.



 REFERENCES

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.
Crossref

  
 

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. 

View

  
 

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

  

 




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