2-absorbing hyperideals and homomorphisms in join hyperlattices


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Authors

  • Harikrishnan P K Manipal Institute of Technology, Manipal Academy of Higher Education
  • Pallavi P Manipal Institute of Technology, Manipal Academy of Higher Education
  • Madeline Al-Tahan Manipal Institute of Technology, Manipal Academy of Higher Education
  • Vadiraja B Manipal Institute of Technology, Manipal Academy of Higher Education
  • S P Kuncham Manipal Institute of Technology, Manipal Academy of Higher Education

Keywords:

prime hyperideal, Hyperlattice, radical

Abstract

In this paper, we investigate hyperlattices, which arise by replacing one (or both) binary operation(s) of a lattice with hyperoperation(s). Several authors have studied prime generalizations of ideals in rings as well as lattices. We focus  on the prime generalizations of hyperideals in join hyperlattices. Specifically, we introduce the concept of $2$-absorbing, primary $2$-absorbing primary etc.. in join hyperlattices and explore their interrelations. We establish that the intersection of two prime hyperideals is 2-absorbing, and the intersection of two $Q$-primary hyperideals is 2-absorbing primary. Additionally, we deal with the study of homomorphic images and pre-images of various types of hyperideals in join hyperlattices.

Author Biographies

Harikrishnan P K, Manipal Institute of Technology, Manipal Academy of Higher Education

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,

Institute of Eminence & Deemed to be University
Manipal - 576104 | Karnataka | India

Pallavi P, Manipal Institute of Technology, Manipal Academy of Higher Education

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,

Institute of Eminence & Deemed to be University
Manipal - 576104 | Karnataka | India

Madeline Al-Tahan, Manipal Institute of Technology, Manipal Academy of Higher Education

Department of Mathematics and Statistics,
Abu Dhabi University, UAE

Vadiraja B, Manipal Institute of Technology, Manipal Academy of Higher Education

Department of Mathematics,
Manipal Institute of Technology,
Manipal Academy of Higher Education,

Institute of Eminence & Deemed to be University
Manipal - 576104 | Karnataka | India

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Published

2023-11-07

How to Cite

P K, H., P, P., Al-Tahan, M., B, V., & Kuncham, S. P. (2023). 2-absorbing hyperideals and homomorphisms in join hyperlattices. Results in Nonlinear Analysis, 6(4), 128–139. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/273