Module Structures on Hoops

R. A. Borzooei, M. Sabetkish () and M. Aaly Kologani ()
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R. A. Borzooei: Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
M. Sabetkish: Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
M. Aaly Kologani: Hatef Higher Education Institute, Zahedan, Iran

New Mathematics and Natural Computation (NMNC), 2024, vol. 20, issue 03, 601-619

Abstract: In this paper, we apply the theory of modules on hoops and introduce two concepts of modules on hoops and provide special examples and interesting results. Both concepts are correct and logical. The first concept is very close to the definition of module in abstract algebra. In this case, we investigate some important results in modules such as sub-modules and quotient structures. But if we want to investigate the relationship between hoop-modules and other modules on logical algebraic structures such as BCK-modules and MV-modules, we need to define the second definition of hoop-modules. In this case, we can get that a BCK-modules and an MV-module from any hoop-module.

Keywords: Hoop; hoop-module; BCK-algebra; MV-algebra (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S1793005724500339

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