Bulletin of the Belgian Mathematical Society - Simon Stevin

A Generalization of Rickart Modules

Burcu Ungor, Sait Halıcıoglu, and Abdullah Harmanci

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Abstract

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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 21, Number 2 (2014), 303-318.

Dates
First available in Project Euclid: 20 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1400592627

Digital Object Identifier
doi:10.36045/bbms/1400592627

Mathematical Reviews number (MathSciNet)
MR3211018

Zentralblatt MATH identifier
1305.16001

Subjects
Primary: 13C99: None of the above, but in this section 16D40: Free, projective, and flat modules and ideals [See also 19A13] 16D80: Other classes of modules and ideals [See also 16G50]

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

Citation

Ungor, Burcu; Halıcıoglu, Sait; Harmanci, Abdullah. A Generalization of Rickart Modules. Bull. Belg. Math. Soc. Simon Stevin 21 (2014), no. 2, 303--318. doi:10.36045/bbms/1400592627. https://projecteuclid.org/euclid.bbms/1400592627


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