SMARANDACHE ANTI ZERO DIVISORS

Authors

  • Rebin M. Hassan Department of Mathematics, College of Basic Education, University of Raparin, Ranya, Kurdistan Region-Iraq
  • Suham H. Awla Department of Mathematics, College of Education, Salahaddin University, Erbil, Kurdistan Region-Iraq

DOI:

https://doi.org/10.25271/sjuoz.2025.13.1.1342

Keywords:

Zero Divisors, Unit Element, Sazd Element, Sazd Ideal

Abstract

In this paper, we study and discuss the concept of Smarandache anti zero divisor (SAZD) element of the ring  and the group ring , where  is a cyclic group of order  generated by . Moreover, we introduce and discuss the concept of SAZD ideal of the ring . Some results related to the given concepts are proved in detail. Accordingly, a Computer Algebra System (GAP) is used to verify the results of this study

References

Kandasamy, W. V. (2001). Smarandache zero divisors. Department of Mathematics Indian Institute of Technology, Madras.

Kandasamy, W. V. (2002a). Smarandache Ring. American Research Press.

Kandasamy, W. V. (2002b). Smarandache Semirings, Semifields, And Semivector Spaces. American Research Press: Rehoboth, NM, USA.

Kandasamy, W. V., & Chetry, M. K. (2002). Smarandache-Zero Divisors in Group Rings. Department of Mathematics Indian Institute of Technology, Madras.

Padilla, R. (1998). Smarandache algebraic structures. Bulletin of Pure and Applied Sciences, Delhi, 17(1), 119-121.

Smarandache, F. (2000). Special Algebraic Structures, in Collected papers. Abaddaba, Oradea, 3, 78-81.

Srinivas, T., & Rao, A. C. S. (2009). On Smarandache Rings. Scientia Magna, 5(4), 117-124.

The GAP Group (2016). GAP-Groups, Algorithms and programming, Version 4.8.3. http://www.gap-system.org.

Yongxing, W. (2005). Research On Smarandache problem in number theory. Hexis, 2, 103-106.

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Published

2025-01-12

How to Cite

Hassan, R. M., & Awla, S. H. (2025). SMARANDACHE ANTI ZERO DIVISORS. Science Journal of University of Zakho, 13(1), 52–57. https://doi.org/10.25271/sjuoz.2025.13.1.1342

Issue

Vol. 13 No. 1 (2025): January - March Issue

Section

Science Journal of University of Zakho

License

Copyright (c) 2025 Suham H. Awla, Rebin M. Hassan

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