On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and 𝒁𝟐𝒏

Sandra; Stipan

doi:https://doi.org/10.54216/GJMSA.0110205

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Volume 11 • Issue 2 • PP: 37-43 • 2024

On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and 𝒁𝟐𝒏

Sandra Terazic ^1*

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,

Stipan Podobnic ¹

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¹Department of Mathematics, University of Rijeka, City of Rijeka, Croatia

* Corresponding Author.

DOI https://doi.org/10.54216/GJMSA.0110205

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

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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: 𝑈(𝑁𝐶𝑅)𝑍𝑝≅𝑍𝑃−1∝(𝑍𝑃∝𝑍𝑃−1)

𝑈(𝑁𝐶𝑅)2𝑛≅(𝑍2×𝑍2𝑛−2)⋉(𝑍2𝑛⋉(𝑍2×𝑍2𝑛−2)).

Keywords

Group of units NCR ring Rings modulo integers Prime number

References

[1] Ozcek, M. (2024). On the Non-Commutative Logical Rings As Novel Extensions of Neutrosophic Rings. Journal of Neutrosophic and Fuzzy Systems, 23-30. DOI: https://doi.org/10.54216/JNFS.080203.

[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.

[8] Basheer, A., Ahmad, K., and Ali, R., “A Short Contribution to Von Shtawzen's Abelian Group In n-Cyclic Refined Neutrosophic Rings", Journal Of Neutrosophic And Fuzzy Systems, 2022.

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Terazic, Sandra, Podobnic, Stipan. "On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and 𝒁𝟐𝒏." Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 11, no. Issue 2, 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 𝒁𝟐𝒏. Galoitica: Journal of Mathematical Structures and Applications, Volume 11(Issue 2), 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 𝒁𝟐𝒏." Galoitica: Journal of Mathematical Structures and Applications Volume 11, no. Issue 2 (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 𝒁𝟐𝒏', Galoitica: Journal of Mathematical Structures and Applications, Volume 11(Issue 2), pp. 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 𝒁𝟐𝒏. Galoitica: Journal of Mathematical Structures and Applications. 2024;Volume 11(Issue 2):37-43. DOI: https://doi.org/10.54216/GJMSA.0110205

S. Terazic, S. Podobnic, "On The Group of Units Problem of the Non-Commutative Logical Extension of the Rings 𝒁𝒑 and 𝒁𝟐𝒏," Galoitica: Journal of Mathematical Structures and Applications, vol. Volume 11, no. Issue 2, pp. 37-43, 2024. DOI: https://doi.org/10.54216/GJMSA.0110205

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