Extensions of Baer and Principally Projective Modules

Year 2012, Volume: 25 Issue: 4, 863 - 867, 25.02.2012

Sait Halicioglu Burcu Ungor Abdullah Harmancı

Abstract

In this note, we investigate extensions of Baer and principally projective modules. Let R be an arbitrary ring with identity and M a right R-module. For an abelian module M, we show that M is Baer (resp. principally projective) if and only if the polynomial extension of M is Baer (resp. principally projective) if and only if the power series extension of M is Baer (resp. principally projective) if and only if the Laurent polynomial extension of M is Baer (resp. principally projective) if and only if the Laurent power series extension of M is Baer (resp. principally projective). 

Keywords

abelian modules, Baer modules, principally projective modules.

References

• [1] N. Agayev, S. Halicioglu and A. Harmanci, ``On Rickart modules’’, appears in Bull. Iran. Math. Soc. available at http://www. iranjournals.ir/ims/bulletin/
• [2] G. F. Birkenmeier, J. Y. Kim and J. K. Park, ``On extensions of Baer and quasi-Baer Rings’’, J. Pure Appl. Algebra 159(2001), 25-42.
• [3] I. Kaplansky, ``Rings of Operators’’, Math. Lecture Note Series, Benjamin, New York, (1965).
• [4] T. K. Lee and Y. Zhou, ``Reduced modules’’, Rings, modules, algebras, and abelian groups, 365-377, Lecture Notes in Pure Appl. Math. 236, Dekker, New York, (2004).
• [5] S. T. Rizvi and C. S. Roman, ``Baer and QuasiBaer Modules’’, Comm. Algebra 32(2004), 103-123.
• [6] J. E. Roos, ``Sur les categories auto-injectifs a droit’’, C. R. Acad. Sci. Paris 265(1967), 14- 17.