Research Article Open Access

The Algebraic K-Theory of Finitely Generated Projective Supermodules P(R) Over a Supercommutative Super-Ring R

Ameer Jaber

Abstract

Problem statement: Algebraic K-theory of projective modules over commutative rings were introduced by Bass and central simple superalgebras, supercommutative super-rings were introduced by many researchers such as Knus, Racine and Zelmanov. In this research, we classified the projective supermodules over (torsion free) supercommutative super-rings and through out this study we forced our selves to generalize the algebraic K-theory of projective supermodules over (torsion free) supercommutative super-rings. Approach: We generalized the algebraic K-theory of projective modules to the super-case over (torsion free) supercommutative super-rings. Results: we extended two results proved by Saltman to the supercase. Conclusion: The extending two results, which were proved by Saltman, to the supercase and the algebraic K-theory of projective supermodules over (torsion free) supercommutative super-rings would help any researcher to classify further properties about projective supermodules.

Journal of Mathematics and Statistics
Volume 5 No. 3, 2009, 171-177

DOI: https://doi.org/10.3844/jmssp.2009.171.177

Submitted On: 6 October 2008 Published On: 30 September 2009

How to Cite: Jaber, A. (2009). The Algebraic K-Theory of Finitely Generated Projective Supermodules P(R) Over a Supercommutative Super-Ring R . Journal of Mathematics and Statistics, 5(3), 171-177. https://doi.org/10.3844/jmssp.2009.171.177

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Keywords

  • Projective supermodules
  • superinvolutions
  • brauer groups
  • brauer-wall groups