Article in press
Authors:
Title:
Decomposable and strongly decomposable almost distributive lattices
PDFSource:
Discussiones Mathematicae - General Algebra and Applications
Received: 2024-09-15 , Revised: 2025-01-14 , Accepted: 2025-01-14 , Available online: 2025-10-01 , https://doi.org/10.7151/dmgaa.1492
Abstract:
The concepts of Decomposable and Strongly decomposable almost distributive lattices are introduced. Various properties of prime, minimal prime and annihilator ideals of a decomposable ADL are furnished. Some characterizations for an ideal in a strongly decomposable ADL to be totally ordered are provided.
Keywords:
Almost Distributive Lattice (ADL), prime ideal, minimal prime ideal, maximal ideal, annihilator ideal, Decomposable ADL, Strongly decomposable ADL
References:
- W.H. Cornish, Normal lattices, J. Australian Math. Soc. 14(2) (1972) 200–215.
https://doi.org/10.1017/S1446788700010041 - G. Gratzer and E.T. Schmidt, Characterizations of relatively complemented distributive lattices, Publ. Math. (Debrecen) 5 (1958) 275–287.
https://doi.org/10.5486/PMD.1958.5.3-4.11 - X. M. Lu, D.S. Liu, Z.N. Qi and H.R. Qin, Prime ideals in decomposable lattices (2010).
arXiv: 1006.3850 - Y.S. Pawar, Characterizations of normal lattices, Indian J. Pure Appl. Math. 24 (1993) 651–656.
- Y.S. Pawar and I.A. Shaikh, The space of maximal ideals in an almost distributive lattice, Int. Math. Forum 6 (2011) 1387–1396.
- Y.S. Pawar and I.A. Shaikh, On prime, minimal prime and annihilator ideals in an almost distributive lattice, Eur. J Pure Appl. Math. 6(1) (2013) 107–118.
- N. Rafi, Ravi Kumar Bandaru and M. Srujana, $\mathcal{N}$-prime spectrum of Stone almost distributive lattices, Discuss. Math. Gen. Algebra Appl. 41(2) (2021) 299–320.
https://doi.org/10.7151/dmgaa.1370 - N. Rafi, T.S. Rao and M. Srujana, Disjunctive ideals of almost distributive lattices, Discuss. Math. Gen. Algebra Appl. 42(1) (2022) 159–178.
https://doi.org/10.7151/dmgaa.1384 - G.C. Rao and M. Sambasiva Rao, Annihilator ideals in almost distributive lattices, Int. Math. Forum 4 (2009) 733–746.
- G.C. Rao and M. Sambasiva Rao, $\alpha$-ideals and prime ideals in ADL, Int. J. Algebra 3 (2009) 221–229.
- G.C. Rao and S. Ravikumar, Normal almost distributive lattices, Soutest Asian Bull. Math. 32 (2008) 831–841.
- G.C. Rao and S. Ravikumar, Minimal prime ideals in almost distributive lattices, Int. J. Math. Sciences 4 (2009) 475–484.
- U.M. Swamy and G.C. Rao, Almost distributive lattices, J. Austral. Math. Soc. 31 (1981) 77–91.
https://doi.org/10.1017/S1446788700018498 - U.M. Swamy, S. Ramesh and Ch. Shanti Sundar Raj, Prime Ideal Characterization of stone ADLS, Asian Eur. J. Math. 3(2) (2010) 357–367.
https://doi.org/10.1142/S179355711000026X
Close