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MODULES WITH FI-EXTENDING HULLS

Published online by Cambridge University Press:  01 May 2009

GARY F. BIRKENMEIER,
JAE KEOL PARK and
S. TARIQ RIZVI
GARY F. BIRKENMEIER
Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, USA e-mail: gfb1127@louisiana.edu
JAE KEOL PARK
Affiliation:
Department of Mathematics, Busan National University, Busan 609-735, South Korea e-mail: jkpark@pusan.ac.kr
S. TARIQ RIZVI
Affiliation:
Department of Mathematics, Ohio State University, Lima, OH 45804-3576, USA e-mail: rizvi.1@osu.edu
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Abstract

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It is shown that every finitely generated projective module PR over a semiprime ring R has the smallest FI-extending essential module extension $H_{\frak{FI}}(P_R)$ (called the absolute FI-extending hull of PR) in a fixed injective hull of PR. This module hull is explicitly described. It is proved that $\widehat{Q}_{\frak{FI}}({\rm End}(P_R))\cong {\rm End}(H_{\frak{FI}}(P_R))$, where $\widehat{Q}_{\frak{FI}}({\rm End}(P_R))$ is the smallest right FI-extending right ring of quotients of End(PR) (in a fixed maximal right ring of quotients of End(PR). Moreover, we show that a finitely generated projective module PR over a semiprime ring R is FI-extending if and only if it is a quasi-Baer module and if and only if End(PR) is a quasi-Baer ring. An application of this result to C*-algebras is considered. Various examples which illustrate and delimit the results of this paper are provided.

Keywords

Primary 16N6016D40Secondary 16S50

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 2 , May 2009, pp. 347 - 357
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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