Galoitica: Journal of Mathematical Structures and Applications

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Volume 11 , Issue 2 , PP: 37-43, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’

Sandra Terazic 1 * , Stipan Podobnic 2

  • 1 Department of Mathematics, University of Rijeka, City of Rijeka, Croatia - (Stipanpod133@Uniri.hr)
  • 2 Department of Mathematics, University of Rijeka, City of Rijeka, Croatia - (Sandy1997te@Uniri.hr)
  • Doi: https://doi.org/10.54216/GJMSA.0110205

    Received: December 14, 2023 Revised: April 10, 2024 Accepted: July 29, 2024
    Abstract

    This paper is dedicated to studying the group of units problem of the non-commutative logical extension of two different rings 𝑍𝑝 and 𝑍2𝑛, where we classify the group of units of these rings as semi-direct products of well-known abelian groups as follows: π‘ˆ(𝑁𝐢𝑅)𝑍𝑝≅𝑍𝑃−1∝(𝑍𝑃∝𝑍𝑃−1)

    π‘ˆ(𝑁𝐢𝑅)2𝑛≅(𝑍2×𝑍2𝑛−2)⋉(𝑍2𝑛⋉(𝑍2×𝑍2𝑛−2)).

    Keywords :

    Group of units , NCR ring , Rings modulo integers , Prime number

    References

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    [2] Osagie, A. (2024). On The Algebraic Classification of the 4-Cyclic Refined Neutrosophic Real Roots of Unity Group. Galoitica: Journal of Mathematical Structures and Applications, 28-36. DOI: https://doi.org/10.54216/GJMSA.0110204

    [3] Nabil Khuder Salman, Maikel Leyva Vazquez,Batista Hernández Noel. On The Classification of 3-Cyclic/4-Cyclic Refined Neutrosophic Real and Rational Von Shtawzen's Group. International Journal of Neutrosophic Science, (2024); 23 (2): 26-31.

    [4] Sadiq. B., “A Contribution To The group Of Units Problem in Some 2-Cyclic Refined Neutrosophic Rings ", International Journal of Neutrosophic Science, 2022.

    [5] Sankari, H., and Abobala, M., “On the Classification of the Group of Units of Rational and Real 2-Cyclic Refined Neutrosophic Rings", Neutrosophic Sets and Systems, 2023.

    [6] Sankari, H., and Abobala, M., “On the Group of Units Classification In 3-Cyclic and 4-cyclic Refined Rings of Integers and the Proof of Von Shtawzens' Conjectures", International Journal of Neutrosophic Science, 2023.

    [7] Von Shtawzen, O., “On a Novel Group Derived from a Generalization of Integer Exponents and Open Problems", Galoitica journal Of Mathematical Structures and Applications, Vol 1, 2022.

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    Cite This Article As :
    Terazic, Sandra. , Podobnic, Stipan. On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’. Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , 2024, pp. 37-43. DOI: https://doi.org/10.54216/GJMSA.0110205
    Terazic, S. Podobnic, S. (2024). On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’. Galoitica: Journal of Mathematical Structures and Applications, (), 37-43. DOI: https://doi.org/10.54216/GJMSA.0110205
    Terazic, Sandra. Podobnic, Stipan. On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’. Galoitica: Journal of Mathematical Structures and Applications , no. (2024): 37-43. DOI: https://doi.org/10.54216/GJMSA.0110205
    Terazic, S. , Podobnic, S. (2024) . On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’. Galoitica: Journal of Mathematical Structures and Applications , () , 37-43 . DOI: https://doi.org/10.54216/GJMSA.0110205
    Terazic S. , Podobnic S. [2024]. On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’. Galoitica: Journal of Mathematical Structures and Applications. (): 37-43. DOI: https://doi.org/10.54216/GJMSA.0110205
    Terazic, S. Podobnic, S. "On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and π’πŸπ’," Galoitica: Journal of Mathematical Structures and Applications, vol. , no. , pp. 37-43, 2024. DOI: https://doi.org/10.54216/GJMSA.0110205