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FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS

Year 2019, , 64 - 76, 08.01.2019
https://doi.org/10.24330/ieja.504114

Abstract

Ideals that share properties with the Frattini ideal of a Leibniz
algebra are studied. Similar investigations have been considered in group the-
ory. The results will hold for Lie algebras as well. Many of the results involve
nilpotency of these algebras.

References

  • Sh. A. Ayupov and B. A. Omirov, On Leibniz algebras, Algebra and operator theory (Tashkent, 1997), Kluwer Acad. Publ., Dordrecht, (1998), 1-12.
  • D. W. Barnes, Some theorems on Leibniz algebras, Comm. Algebra, 39(7) (2011), 2463-2472.
  • D. W. Barnes, Schunck classes of soluble Leibniz algebras, Comm. Algebra, 41(11) (2013), 4046-4065.
  • C. Batten, L. Bosko-Dunbar, A. Hedges, J. T. Hird, K. Stagg and E. Stitzinger, A Frattini Theory for Leibniz algebras, Comm. Algebra, 41(4) (2013), 1547- 1557.
  • C. Batten Ray, A. Combs, N. Gin, A. Hedges, J. T. Hird and L. Zack, Nilpotent Lie and Leibniz algebras, Comm. Algebra, 42(6) (2014), 2404-2410.
  • C. Batten Ray, A. Hedges and E. Stitzinger, Classifying several classes of Leibniz algebras, Algebr. Represent. Theory, 17(2) (2014), 703-712.
  • J. C. Beidleman and T. K. Seo, Generalized Frattini subgroups of nite groups, Paci c J. Math., 23 (1967), 441-450.
  • L. Bosko, A. Hedges, J. T. Hird, N. Schwartz and K. Stagg, Jacobson's re ne- ment of Engel's theorem for Leibniz algebras, Involve, 4(3) (2011), 293-296.
  • T. Burch, M. Harris, A. McAlister, E. Rogers, E. Stitzinger and S. M. Sullivan, 2-recognizeable classes of Leibniz algebras, J. Algebra, 423 (2015), 506-513.
  • I. Demir, K. Misra and E. Stitzinger, On some structures of Leibniz algebras, Recent advances in representation theory, quantum groups, algebraic geometry, and related topics, Amer. Math. Soc., Providence, RI, Contemp. Math., 623 (2014), 41-54.
  • L.-C. Kappe and J. Kirkland, Some analogues of the Frattini subgroup, Algebra Colloq., 4(4) (1997), 419-426.
  • J.-L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Enseign. Math., 39 (1993), 269-293.
  • K. Stagg, Analogues of the Frattini subalgebra, Int. Electron. J. Algebra, 9 (2011), 124-132.
  • D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc., 27 (1973), 440-462.
  • D. Towers, Two ideals of an algebra closely related to its Frattini ideal, Arch. Math. (Basel), 35(1-2) (1980), 112-120.
Year 2019, , 64 - 76, 08.01.2019
https://doi.org/10.24330/ieja.504114

Abstract

References

  • Sh. A. Ayupov and B. A. Omirov, On Leibniz algebras, Algebra and operator theory (Tashkent, 1997), Kluwer Acad. Publ., Dordrecht, (1998), 1-12.
  • D. W. Barnes, Some theorems on Leibniz algebras, Comm. Algebra, 39(7) (2011), 2463-2472.
  • D. W. Barnes, Schunck classes of soluble Leibniz algebras, Comm. Algebra, 41(11) (2013), 4046-4065.
  • C. Batten, L. Bosko-Dunbar, A. Hedges, J. T. Hird, K. Stagg and E. Stitzinger, A Frattini Theory for Leibniz algebras, Comm. Algebra, 41(4) (2013), 1547- 1557.
  • C. Batten Ray, A. Combs, N. Gin, A. Hedges, J. T. Hird and L. Zack, Nilpotent Lie and Leibniz algebras, Comm. Algebra, 42(6) (2014), 2404-2410.
  • C. Batten Ray, A. Hedges and E. Stitzinger, Classifying several classes of Leibniz algebras, Algebr. Represent. Theory, 17(2) (2014), 703-712.
  • J. C. Beidleman and T. K. Seo, Generalized Frattini subgroups of nite groups, Paci c J. Math., 23 (1967), 441-450.
  • L. Bosko, A. Hedges, J. T. Hird, N. Schwartz and K. Stagg, Jacobson's re ne- ment of Engel's theorem for Leibniz algebras, Involve, 4(3) (2011), 293-296.
  • T. Burch, M. Harris, A. McAlister, E. Rogers, E. Stitzinger and S. M. Sullivan, 2-recognizeable classes of Leibniz algebras, J. Algebra, 423 (2015), 506-513.
  • I. Demir, K. Misra and E. Stitzinger, On some structures of Leibniz algebras, Recent advances in representation theory, quantum groups, algebraic geometry, and related topics, Amer. Math. Soc., Providence, RI, Contemp. Math., 623 (2014), 41-54.
  • L.-C. Kappe and J. Kirkland, Some analogues of the Frattini subgroup, Algebra Colloq., 4(4) (1997), 419-426.
  • J.-L. Loday, Une version non commutative des algebres de Lie: les algebres de Leibniz, Enseign. Math., 39 (1993), 269-293.
  • K. Stagg, Analogues of the Frattini subalgebra, Int. Electron. J. Algebra, 9 (2011), 124-132.
  • D. A. Towers, A Frattini theory for algebras, Proc. London Math. Soc., 27 (1973), 440-462.
  • D. Towers, Two ideals of an algebra closely related to its Frattini ideal, Arch. Math. (Basel), 35(1-2) (1980), 112-120.
There are 15 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Allison Mcalister This is me

Kristen Stagg Rovira This is me

Ernie Stitzinger

Publication Date January 8, 2019
Published in Issue Year 2019

Cite

APA Mcalister, A., Rovira, K. S., & Stitzinger, E. (2019). FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS. International Electronic Journal of Algebra, 25(25), 64-76. https://doi.org/10.24330/ieja.504114
AMA Mcalister A, Rovira KS, Stitzinger E. FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS. IEJA. January 2019;25(25):64-76. doi:10.24330/ieja.504114
Chicago Mcalister, Allison, Kristen Stagg Rovira, and Ernie Stitzinger. “FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra 25, no. 25 (January 2019): 64-76. https://doi.org/10.24330/ieja.504114.
EndNote Mcalister A, Rovira KS, Stitzinger E (January 1, 2019) FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS. International Electronic Journal of Algebra 25 25 64–76.
IEEE A. Mcalister, K. S. Rovira, and E. Stitzinger, “FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS”, IEJA, vol. 25, no. 25, pp. 64–76, 2019, doi: 10.24330/ieja.504114.
ISNAD Mcalister, Allison et al. “FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra 25/25 (January 2019), 64-76. https://doi.org/10.24330/ieja.504114.
JAMA Mcalister A, Rovira KS, Stitzinger E. FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS. IEJA. 2019;25:64–76.
MLA Mcalister, Allison et al. “FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS”. International Electronic Journal of Algebra, vol. 25, no. 25, 2019, pp. 64-76, doi:10.24330/ieja.504114.
Vancouver Mcalister A, Rovira KS, Stitzinger E. FRATTINI PROPERTIES AND NILPOTENCY IN LEIBNIZ ALGEBRAS. IEJA. 2019;25(25):64-76.