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2024 | OriginalPaper | Chapter

8. On Rickart and Baer Semimodules

Authors : Mamadou Lamine Diallo, Jean Raoult Tsiba, Djiby Sow

Published in: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence

Publisher: Springer Nature Switzerland

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Abstract

This chapter generalizes the Rickart (resp., Baer) property on semirings and semimodules. We introduce weak Rickart (resp., Baer ) semimodules and then identify i-Rickart semimodules as a specific subclass of the former. Basic links between the different Baer and Rickart semimodules are discussed. A characterization of the Rickart semimodules by their endomorphism semiring is provided.

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previous chapter A Perturbed Mann-Type Algorithm for Zeros of Maximal Monotone Mappings

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Abuhlail, Jawad and Noegraha, Rangga Ganzar On k-Noetherian and k-Artinian semirings, journal=arXiv preprint arXiv:1907.06149, 2019;

Armendariz, Efraim P. A note on extensions of Baer and PP-rings. Journal of the Australian Mathematical Society,18,4,470–473,1974,Cambridge University Press;

Bergman, George M. Hereditary commutative rings and centres of hereditary rings, Proceedings of the London Mathematical Society,3,2,214–236,1971,Wiley Online Library;

Birkenmeier, Gary F and Park, Jae Keol and Rizvi, S Tariq. Extensions of rings and modules. 2013,Springer;

Clark, W Edwin and others. Twisted matrix units semigroup algebras. Duke Mathematical Journal,34,3,Duke University Press;

Endo, Shizuo, Note on PP Rings:(A Supplement to Hattori’s Paper), Nagoya Mathematical Journal,17,167–170,1960, Cambridge University Press

Evans, Michael, On commutative PP rings Pacific Journal of mathematics,41,3,687–697,1972,Mathematical Sciences Publishers;

Gupta, V and Chaudhari, JN and Kumar, P.: STRONGLY BAER AND STRONGLY QUASI-BAER SEMIRINGS AND GENERALIZATIONS. Asian-European Journal of Mathematics,2,04,579–591,2009,World Scientific;

Golan, Jonathan S. Semirings and their Applications. 2013,Springer Science & Business Media;

10.

Hattori, Akira A foundation of torsion theory for modules over general rings, Nagoya Mathematical Journal,17,147–158,1960,Cambridge University Press;

11.

Juber, Alaa Zakaria PROPERTIES OF APP-RINGS 2008, The University of Jordan;

12.

Kaplansky, Irving, Rings of operators,1968,WA Benjamin;

13.

Lam, TY. A First course in noncommutative rings, GTM 131 (1991),Springer-Verlag;

14.

Lam, Tsit-Yuen. Lectures on modules and rings. 189,2012,Springer Science & Business Media;

15.

Lee, Gangyong and Tariq Rizvi, S and Roman, Cosmin S. Rickart modules Communications in Algebra,38,11,4005–4027,2010,Taylor & Francis;

16.

Lee, Gangyong, Theory of Rickart modules, 2010,The Ohio State University;

17.

Maeda, Shûichirô and others, On a ring whose principal right ideals generated by idempotents form a lattice Journal of Science of the Hiroshima University, Series A (Mathematics, Physics, Chemistry),24,3,509–525,1960,Hiroshima University, Department of Mathematics;

18.

Rizvi, S Tariq and Roman, Cosmin S, Baer and quasi-Baer modules, Communications in Algebra,32,1,103–123,2004,Taylor & Francis;

19.

Small, Lance W, Semihereditary rings, Bulletin of the American Mathematical Society,73,5,656–658,1967,American Mathematical Society;

20.

Wisbauer, Robert, Foundations of module and ring theory, 2018,Routledge;

21.

Zelmanowitz, J, Regular modules, Transactions of the American Mathematical Society,163,341–355,1972;MathSciNetCrossRef

22.

Khuri, SM, Endomorphism rings of modules, Khuri, SM,2004,manuscript;

Title: On Rickart and Baer Semimodules
Authors: Mamadou Lamine Diallo
Jean Raoult Tsiba
Djiby Sow
Publisher: Springer Nature Switzerland
Book: Mathematics of Computer Science, Cybersecurity and Artificial Intelligence
Print ISBN: 978-3-031-66221-8

Electronic ISBN: 978-3-031-66222-5

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-3-031-66222-5_8

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