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On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications

Year 2017, Volume: 5 Issue: 4, 148 - 155, 01.10.2017

Osman Avcioglu İbrahim Ilker Akca

Abstract


Keywords

Algebroid crossed module Peiffer ideal

References

  • M. Alp, Pullback crossed modules of algebroids, Iran. J. Sci. Technol. (Sciences) 32 (1) (2008) 1–5.
  • M. Alp, Pushout crossed modules of algebroids, Iran. J. Sci. Technol. (Sciences) 32 (3) (2008) 175–181.
  • S. M. Amgott, Separable categories, J. Pure Appl. Algebra 40 (1986) 1–14.
  • O. Avcıoğlu, İ. İ. Akça, Free modules and crossed modules of R-algebroids, Under review.
  • O. Avcıoğlu, İ. İ. Akça, On pullback and induced crossed modules of R-algebroids, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 (2) (2017) 225-242.
  • O. Avcıoğlu, İ. İ. Akça, Coproduct of crossed modules of R-algebroids, presented in ’2nd International Conference on Advances in Natural and Applied Sciences, ICANAS 2017, Antalya, Turkey, April 18-21, 2017’.
  • H. J. Baues, D. Conduché, The central series for Peiffer commutators in groups with operators, J. Algebra 133 (1) (1990) 1–34.
  • R. Brown, J. Huebschmann, Identities among relations. Low dimensional topology (Bangor, 1979), London Math. Soc. Lecture Note Ser. 48, Cambridge Univ Press, Cambridge (1982) 153–202.
  • R. Brown, P. J. Higgins, R. Sivera, Nonabelian Algebraic Topology. EMS Tracts in Mathematics Vol.15, 2011.
  • B. Mitchell, Rings with several objects, Advances in Mathematics 8(1) (1972) 1-161.
  • B. Mitchell, Some applications of module theory to functor categories, Bull. Amer. Math. Soc. 84 (1978) 867– 885.
  • B. Mitchell, Separable Algebroids, Mem. Amer. Math. Soc. 57 (1985), no. 333, 96 pp.
  • G. H. Mosa, Higher dimensional algebroids and crossed complexes, PhD Thesis, University College of North Wales, Bangor, 1986.
  • N. M. Shammu, Algebraic and categorical structure of categories of crossed modules of algebras, PhD Thesis, University College of North Wales, Bangor, 1992.
  • R. Peiffer, ‘Über Identitäten zwischen Relationen’, Math. Ann. 121 (1949) 67–99.
  • J. H. C. Whitehead, On adding relations to homotopy groups, Annals of Mathematics 42 (2) (1941) 409–428.
  • J. H. C. Whitehead, Note on a previous paper entitled "On adding relations to homotopy groups.", Annals of Mathematics 47 (4) (1946) 806–810.

Year 2017, Volume: 5 Issue: 4, 148 - 155, 01.10.2017

Osman Avcioglu İbrahim Ilker Akca

Abstract

References

  • M. Alp, Pullback crossed modules of algebroids, Iran. J. Sci. Technol. (Sciences) 32 (1) (2008) 1–5.
  • M. Alp, Pushout crossed modules of algebroids, Iran. J. Sci. Technol. (Sciences) 32 (3) (2008) 175–181.
  • S. M. Amgott, Separable categories, J. Pure Appl. Algebra 40 (1986) 1–14.
  • O. Avcıoğlu, İ. İ. Akça, Free modules and crossed modules of R-algebroids, Under review.
  • O. Avcıoğlu, İ. İ. Akça, On pullback and induced crossed modules of R-algebroids, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 66 (2) (2017) 225-242.
  • O. Avcıoğlu, İ. İ. Akça, Coproduct of crossed modules of R-algebroids, presented in ’2nd International Conference on Advances in Natural and Applied Sciences, ICANAS 2017, Antalya, Turkey, April 18-21, 2017’.
  • H. J. Baues, D. Conduché, The central series for Peiffer commutators in groups with operators, J. Algebra 133 (1) (1990) 1–34.
  • R. Brown, J. Huebschmann, Identities among relations. Low dimensional topology (Bangor, 1979), London Math. Soc. Lecture Note Ser. 48, Cambridge Univ Press, Cambridge (1982) 153–202.
  • R. Brown, P. J. Higgins, R. Sivera, Nonabelian Algebraic Topology. EMS Tracts in Mathematics Vol.15, 2011.
  • B. Mitchell, Rings with several objects, Advances in Mathematics 8(1) (1972) 1-161.
  • B. Mitchell, Some applications of module theory to functor categories, Bull. Amer. Math. Soc. 84 (1978) 867– 885.
  • B. Mitchell, Separable Algebroids, Mem. Amer. Math. Soc. 57 (1985), no. 333, 96 pp.
  • G. H. Mosa, Higher dimensional algebroids and crossed complexes, PhD Thesis, University College of North Wales, Bangor, 1986.
  • N. M. Shammu, Algebraic and categorical structure of categories of crossed modules of algebras, PhD Thesis, University College of North Wales, Bangor, 1992.
  • R. Peiffer, ‘Über Identitäten zwischen Relationen’, Math. Ann. 121 (1949) 67–99.
  • J. H. C. Whitehead, On adding relations to homotopy groups, Annals of Mathematics 42 (2) (1941) 409–428.
  • J. H. C. Whitehead, Note on a previous paper entitled "On adding relations to homotopy groups.", Annals of Mathematics 47 (4) (1946) 806–810.
There are 17 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Osman Avcioglu This is me

İbrahim Ilker Akca This is me

Publication Date October 1, 2017
Published in Issue Year 2017 Volume: 5 Issue: 4

Cite

APA Avcioglu, O., & Ilker Akca, İ. (2017). On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications. New Trends in Mathematical Sciences, 5(4), 148-155.
AMA Avcioglu O, Ilker Akca İ. On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications. New Trends in Mathematical Sciences. October 2017;5(4):148-155.
Chicago Avcioglu, Osman, and İbrahim Ilker Akca. “On Generators of Peiffer Ideal of a Pre-R-Algebroid in a Precrossed Module and Applications”. New Trends in Mathematical Sciences 5, no. 4 (October 2017): 148-55.
EndNote Avcioglu O, Ilker Akca İ (October 1, 2017) On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications. New Trends in Mathematical Sciences 5 4 148–155.
IEEE O. Avcioglu and İ. Ilker Akca, “On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications”, New Trends in Mathematical Sciences, vol. 5, no. 4, pp. 148–155, 2017.
ISNAD Avcioglu, Osman - Ilker Akca, İbrahim. “On Generators of Peiffer Ideal of a Pre-R-Algebroid in a Precrossed Module and Applications”. New Trends in Mathematical Sciences 5/4 (October 2017), 148-155.
JAMA Avcioglu O, Ilker Akca İ. On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications. New Trends in Mathematical Sciences. 2017;5:148–155.
MLA Avcioglu, Osman and İbrahim Ilker Akca. “On Generators of Peiffer Ideal of a Pre-R-Algebroid in a Precrossed Module and Applications”. New Trends in Mathematical Sciences, vol. 5, no. 4, 2017, pp. 148-55.
Vancouver Avcioglu O, Ilker Akca İ. On generators of Peiffer ideal of a pre-R-algebroid in a precrossed module and applications. New Trends in Mathematical Sciences. 2017;5(4):148-55.
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