Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-30T19:50:07.319Z Has data issue: false hasContentIssue false
  • English
  • Français

SYMMETRIC ALGEBRAS OVER RINGS AND FIELDS

Part of: Modules, bimodules and ideals Basic linear algebra

Published online by Cambridge University Press:  06 September 2013

THOMAS C. CRAVEN  and
TARA L. SMITH
THOMAS C. CRAVEN*
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, HI 96822, Hawaii
TARA L. SMITH
Affiliation:
Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221–0025, Ohio email [email protected]
*
✉[email protected]
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.

Connections between annihilators and ideals in Frobenius and symmetric algebras are used to provide a new proof of a result of Nakayama on quotient algebras, and an application is given to central symmetric algebras.

Keywords

symmetric algebraFrobenius

MSC classification

Secondary: 16D99: None of the above, but in this section 15A63: Quadratic and bilinear forms, inner products
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 89 , Issue 3 , June 2014 , pp. 466 - 472
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

References

Curtis, C. W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras (Interscience, New York, 1962).Google Scholar
Eilenberg, S. and Nakayama, T., ‘On the dimension of modules and algebras II. Frobenius algebras and quasi-Frobenius rings’, Nagoya Math. J. 9 (1955), 1–16.Google Scholar
Lam, T. Y., Lectures on Modules and Rings (Springer, New York, 1999).CrossRefGoogle Scholar
Nakayama, T., ‘On Frobeniusean algebras. I’, Ann. of Math. (2) 40 (1939), 611–633.CrossRefGoogle Scholar
V. L. Popov (originator), ‘Bilinear mapping’, Encyclopedia of Mathematics, http://www.encyclopediaofmath.org/index.php?title=Bilinear_mapping&oldid=13044.Google Scholar
Wood, J. A., ‘Duality for modules over finite rings and applications to coding theory’, Amer. J. Math. 121 (1999), 555–575.CrossRefGoogle Scholar
Wood, J. A., ‘Anti-isomorphisms, character modules and self-dual codes over non-commutative rings’, Int. J. Inf. Coding Theory 1 (4) (2010), 429–444.Google Scholar