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: 254


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.
  • Google Scholar

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


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.


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



The authors have not declared any conflict of interests.


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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.


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