Open Access
may 2014 A Generalization of Rickart Modules
Burcu Ungor, Sait Halıcıoglu, Abdullah Harmanci
Bull. Belg. Math. Soc. Simon Stevin 21(2): 303-318 (may 2014). DOI: 10.36045/bbms/1400592627


Let $R$ be an arbitrary ring with identity and $M$ a right $R$-module with $S=$ End$_R(M)$. In this paper we introduce $\pi$-Rickart modules as a generalization of Rickart modules. $\pi$-Rickart modules are also a dual notion of dual $\pi$-Rickart modules and extends that of generalized right principally projective rings to the module theoretic setting. The module $M$ is called {\it $\pi$-Rickart} if for any $f\in S$, there exist $e^2=e\in S$ and a positive integer $n$ such that $r_M(f^n)=$ Ker$f^n=eM$. We obtain several results about generalized right principally projective rings by using $\pi$-Rickart modules. Moreover, we investigate relations between a $\pi$-Rickart module and its endomorphism ring.


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Burcu Ungor. Sait Halıcıoglu. Abdullah Harmanci. "A Generalization of Rickart Modules." Bull. Belg. Math. Soc. Simon Stevin 21 (2) 303 - 318, may 2014.


Published: may 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1305.16001
MathSciNet: MR3211018
Digital Object Identifier: 10.36045/bbms/1400592627

Primary: 13C99 , 16D40 , 16D80

Keywords: $\pi$-Rickart module , Fitting module , generalized right principally projective ring , Rickart module

Rights: Copyright © 2014 The Belgian Mathematical Society

Vol.21 • No. 2 • may 2014
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