A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal

Filiz Çıtak; İbrahim Halil Kanat

doi:10.28979/jarnas.1880226

A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal

Abstract

In this paper, we introduce some new structures such as soft primary int-ideal and soft 1-absorbing primary int-ideal, which are different generalizations of the soft prime int-ideal. We study these new structures theoretically and practically. We examine the relationship between these new structures. One of our most important results is that a soft prime int-ideal is both soft primary int-ideal and soft $1$-absorbing primary int-ideal. It is shown with the help of examples that opposites are not always true. Moreover, We show that every soft primary int-ideal is a soft 1-absorbing primary int-ideal, but the opposite of this situation is not validated. Then, another result is the behavior of the soft radical on these structures. Besides, we strengthen this structure through various problems. Moreover, we determine that soft homomorphic images and pre-images of these new structures are guarded under onto ring homomorphisms.

Keywords

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Details

Primary Language

English

Subjects

Algebra and Number Theory, Mathematical Logic, Set Theory, Lattices and Universal Algebra

Journal Section

Research Article

Authors

Filiz Çıtak ^*
0000-0003-1784-1845
Türkiye

İbrahim Halil Kanat
0009-0000-6906-9020
Türkiye

Publication Date

March 30, 2026

Submission Date

February 2, 2026

Acceptance Date

March 5, 2026

Published in Issue

Year 2026 Volume: 12 Number: 1

DOI

https://doi.org/10.28979/jarnas.1880226

IZ

https://izlik.org/JA66FW24ZC

Cite

RIS / Bibtex

APA

Çıtak, F., & Kanat, İ. H. (2026). A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal. Journal of Advanced Research in Natural and Applied Sciences, 12(1), 91-102. https://doi.org/10.28979/jarnas.1880226

AMA

1.Çıtak F, Kanat İH. A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal. JARNAS. 2026;12(1):91-102. doi:10.28979/jarnas.1880226

Chicago

Çıtak, Filiz, and İbrahim Halil Kanat. 2026. “A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal”. Journal of Advanced Research in Natural and Applied Sciences 12 (1): 91-102. https://doi.org/10.28979/jarnas.1880226.

EndNote

Çıtak F, Kanat İH (March 1, 2026) A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal. Journal of Advanced Research in Natural and Applied Sciences 12 1 91–102.

IEEE

[1]F. Çıtak and İ. H. Kanat, “A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal”, JARNAS, vol. 12, no. 1, pp. 91–102, Mar. 2026, doi: 10.28979/jarnas.1880226.

ISNAD

Çıtak, Filiz - Kanat, İbrahim Halil. “A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal”. Journal of Advanced Research in Natural and Applied Sciences 12/1 (March 1, 2026): 91-102. https://doi.org/10.28979/jarnas.1880226.

JAMA

1.Çıtak F, Kanat İH. A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal. JARNAS. 2026;12:91–102.

MLA

Çıtak, Filiz, and İbrahim Halil Kanat. “A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal”. Journal of Advanced Research in Natural and Applied Sciences, vol. 12, no. 1, Mar. 2026, pp. 91-102, doi:10.28979/jarnas.1880226.

Vancouver

1.Filiz Çıtak, İbrahim Halil Kanat. A New Approach to Soft Prime Int-Ideal: Soft Primary Int-Ideal and Soft 1-Absorbing Primary Int-Ideal. JARNAS. 2026 Mar. 1;12(1):91-102. doi:10.28979/jarnas.1880226

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