Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-13T10:12:27.953Z Has data issue: false hasContentIssue false
  • English
  • Français

Decomposability of finite rings

Published online by Cambridge University Press:  09 April 2009

Diane Mainwaring  and
K. R. Pearson
Diane Mainwaring
Affiliation:
La Trobe UniversityBundoora, Victoria 3083, Australia
K. R. Pearson
Affiliation:
La Trobe UniversityBundoora, Victoria 3083, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let p be a prime, let R be a finite p-ring with identity and suppose that the radical of R has pm elements. If R is indecomposable as a ring then there are at most m+1 minimal ideals in R/Rad R.

1980 Mathematics subject classification (Amer. Math. Soc): 16 A 44.

Keywords

Finite ringdecomposablenilpotent p-ringgroup of units.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 2 , September 1979 , pp. 136 - 138
Copyright
Copyright © Australian Mathematical Society 1979

References

Flanigan, F. J. (1973), ‘Radical behaviour and the Wedderburn family’, Bull. Amer. Math. Soc., 79, 66–70.CrossRefGoogle Scholar
Flanigan, F. J. (1974), ‘Radical embedding, genus and toroidal derivations of nilpotent associative algebras’, Bull. Amer. Math. Soc. 80, 986–990.CrossRefGoogle Scholar
Hall, Marshall (1940), ‘The position of the radical in an algebra’, Trans. Amer. Math. Soc. 48, 391–404.CrossRefGoogle Scholar
Jacobson, Nathan (1964), Structure of rings, 2nd ed. (Amer. Math. Soc. Colloq. Publ., Providence).Google Scholar
Mainwaring, Diane (1978), ‘Finite rings with dihedral groups of units’, M.Sc. thesis, La Trobe University.Google Scholar
McDonald, Bernard R. (1974), Finite rings with identity (Marcel Dekker, New York).Google Scholar
Stewart, Ian (1972), ‘Finite rings with a specified group of units’, Math. Z. 126, 51–58 (and 128, 187).CrossRefGoogle Scholar