2-absorbing hyperideals and homomorphisms in join hyperlattices
Abstract views: 166
/ 
PDF downloads: 137
Keywords:
prime hyperideal, Hyperlattice, radicalAbstract
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.
References
R. Ameri, A.M. Bideshki, H.S. Mayerova and A.B. Saeid, Distributive and dual distributive elements in hyperlattices, Analele Universitatii“Ovidius” Constanta-Seria Matematica, 25.3 (2017), 25–36.
B. Davvaz and L.V. Fotea, Hyperring theory and applications, International Academic Press, USA, 2007.
N. Kehayopulu, Correction to the Article:“An introduction to the Theory of Hyperlattices”, Eur. J. Pure Appl. Math, 12.2 (2019), 252–269.
B.B.N. Koguep and C. Lele, On hyperlattices: congruence relations, ideals and homomorphism, Afrika Matematika, 30.1 (2019), 101–111.
B.B.N. Koguep, C. Lele and J.B. Nganou, Normal hyperlattices and pure ideals of hyperlattices, Asian-European Journal of Mathematics, 9.01 (2016), 1650020.
M. Konstantinidou, On P-hyperlattices and their distributivity, Rend. Circ. Mat. Palermo (2), 42.3 (1993), 391–403.
M.A. Konstantinidou and J.E. Mittas, An introduction to the theory of hyperlattices, Math. Balkanica, 7 (1977), 187–193.
A.S. Lashkenari and B. Davvaz, Complete join hyperlattices, Indian J. Pure Appl. Math., 46.5 (2015), 633–645.
P. Pallavi, S.P. Kuncham, G.R.B. Vadiraja and P.K. Harikrishnan, Computation of prime hyperideals in meet hyperlattices, Bull. Comput. Appl. Math., 10.01 (2022).
B.A. Rahnamai, The prime ideal theorem for distributive hyperlattices, Italian journal of pure and applied mathematics, 10 (2001), 75–78.
S. Rasouli and B. Davvaz, Construction and spectral topology on hyperlattices, Mediterr. J. Math., 7.2 (2010), 249–262.
S. Rasouli and B. Davvaz, Lattices derived from hyperlattices, Comm. Algebra, 38.8 (2010), 2720–2737.
S. Tapatee, P.K. Harikrishnan, B.S. Kedukodi and S.P. Kuncham, Graph with respect to superfluous elements in a lattice, Miskolc Math. Notes, (to appear).
S. Tapatee, B.S. Kedukodi, K.P. Shum, P.K. Harikrishnan and S.P. Kun- cham, On essential elements in a lattice and Goldie analogue theorem, Asian- Eur. J. Math., 15.5 (2022), 2250091.
M.P. Wasadikar and K.T. Gaikwad, On 2-absorbing and weakly 2-absorbing ideals of lattices, Mathematical Sciences International Research Journal, 4.2 (2015), 82–85.
M.P. Wasadikar and K.T. Gaikwad, Some properties of 2-absorbing primary ideals in lattices, AKCE Int. J. Graphs Comb., 16.1 (2019), 18–26.
M.P. Wasadikar and K.T. Gaikwad, Some properties of weakly primary and weakly 2-absorbing primary ideals in lattices. Palest. J. Math., 8.1 (2019), 467– 474.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Results in Nonlinear Analysis
This work is licensed under a Creative Commons Attribution 4.0 International License.
