On Inertial Subalgebras of Certain Rings

Sumiyama, Takao

doi:10.1007/978-1-4612-0181-6_26

Takao Sumiyama⁴

Part of the book series: Trends in Mathematics ((TM))

381 Accesses

Abstract

R. Raghavendran, W. E. Clark and R. S. Wilson have proved that finite rings have inertial subalgebras. The author will show that this result is naturally extended to certain infinite rings, and generalize Wedderburn’s theorem concerning commutativity of finite division rings.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Chapter: USD 29.95; Price excludes VAT (USA)

eBook: USD 39.99; Price excludes VAT (USA)

Softcover Book: USD 54.99; Price excludes VAT (USA)

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

References

E. A. Behrens, Ring Theory, Academic Press, New York, 1972.
Google Scholar
W. E. Clark, A coefficient ring for finite non-commutative rings, Proc. Amer. Math. Soc. 33 (1972), 25–28.
MathSciNet MATH Google Scholar
C. W. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras,Pure and Applied Math. Series 11, Inter-science, New York, 1962.
MATH Google Scholar
I. N. Herstein, Noncommutative Rings, Math. Assoc. Amer., Carus Monograph 15, 1968.
Google Scholar
E. C. Ingraham, Inertial subalgebras of algebras over commutative rings,Trans. Amer. Math. Soc. 124 (1966), 77–93.
Article MathSciNet MATH Google Scholar
G. T. Janusz, Separable algebras over commutative rings, Trans. Amer. Math. Soc. 122 (1966), 461–479.
Article MathSciNet MATH Google Scholar
W. Krull, Algebraische Theorie der Ringe II, Math. Ann. 91 (1924), 1–46.
Article MathSciNet MATH Google Scholar
B. R. McDonald, Finite Rings with Identity, Pure and Applied Math. Series 28, Marcel Dekker, New York, 1974.
Google Scholar
R. Raghavendran, Finite associative rings, Compositio Math. 21 (1969), 195–229.
MathSciNet MATH Google Scholar
T. Sumiyama, Coefficient subrings of certain local rings with prime-power characteristic, International J. Math. Math. Sci. 18 (1995), 451–462.
Article MathSciNet MATH Google Scholar
R. S. Wilson, On the structure of finite rings, Compositio Math. 26 (1973), 79–93.
MathSciNet MATH Google Scholar

Download references

Author information

Authors and Affiliations

Department of Mathematics, Aichi Institute of Technology, Toyota, 470-0392, Japan
Takao Sumiyama

Authors

Takao Sumiyama
View author publications
You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA, 70504-1010, USA
Gary F. Birkenmeier
Department of Mathematics, Pusan National University, Pusan, 609-735, Korea
Jae Keol Park
Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea
Young Soo Park

Rights and permissions

Reprints and permissions

Copyright information

About this paper

Cite this paper

Sumiyama, T. (2001). On Inertial Subalgebras of Certain Rings. In: Birkenmeier, G.F., Park, J.K., Park, Y.S. (eds) International Symposium on Ring Theory. Trends in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0181-6_26

Download citation

DOI: https://doi.org/10.1007/978-1-4612-0181-6_26
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6650-1
Online ISBN: 978-1-4612-0181-6
eBook Packages: Springer Book Archive

Publish with us

Policies and ethics