Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Enumeration results in nilpotent algebras

Author: Helmut Strade
Journal: Proc. Amer. Math. Soc. 49 (1975), 20-24
MathSciNet review: 0357526
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: We enumerate the number of subalgebras for some classes of finite nilpotent algebras. These classes are: alternative algebras over $ GF(q)$, noncommutative Jordan algebras over $ GF(q)$, algebras with only zero squares over some Dedekind domain.

References [Enhancements On Off] (What's this?)

  • [1] P. Hall, A contribution to the theory of groups of prime power order, Proc. London Math. Soc. (2) 36 (1934), 29-95.
  • [2] John Knopfmacher, Arithmetical properties of finite rings and algebras, and analytic number theory, J. Reine Angew. Math. 252 (1972), 16–43. MR 0313214
  • [3] J. Knopfmacher and G. E. Burger, Submodules, subalgebras and ideals in finite modules or nilpotent algebras over Dedekind domains, J. London Math. Soc. (2) 5 (1972), 681–690. MR 0313297
  • [4] Robert L. Kruse and David T. Price, Nilpotent rings, Gordon and Breach Science Publishers, New York-London-Paris, 1969. MR 0266956
  • [5] Hel Braun and Max Koecher, Jordan-Algebren, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band 128, Springer-Verlag, Berlin-New York, 1966 (German). MR 0204470

Additional Information

Article copyright: © Copyright 1975 American Mathematical Society