Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 3 , Issue 1 , PP: 14-17, 2023 | Cite this article as | XML | Html | PDF | Full Length Article
Khadija Ben Othman 1 *
Doi: https://doi.org/10.54216/GJMSA.030102
The objective of this paper is to study the Dedekind lattices, where we prove if is a -lattice and domain, then will be a Dedekind domain if and only if every non zero maximal element is invertible.
On the other hand, we prove that if is a domain and -lattices, then is a dedehind domain if and only if is a UFD lattices and every non zero prime element is maximal.
Lattice , UFD , Principal Ideal , Domain , PG-Lattice
[1] Anderson, D. D., Abstract commutative ideal theory without chain condition. Algebra Universalis 6, (1976),
131-145.
[2] Burton, R. G., Fractional elements in multiplicative Lattices. Pacific Journal of Mathematics, vol. 56 , No. 1 ,
(1975) , 35-49 .
[3] Dilworth, R. P., Abstract commutative ideal theory. Pacific Journal of Mathematics, 12 , (1962) , 487 – 498 .
[4] Janowtz, M. F. , Principal Multiplicative Lattices. Pacific Journal of Mathematics, vol. 33 , (1970) , 653 –
656 .
[5] Johnson , E. W. and Johnson , J. A., P-Lattices as ideal Lattices and submodule Lattices., commen. Math.
Univ. San. Pauli., 38 (1989),
21-27 .
[6] McCarthy, P. J. Principal elements of Lattice of ideals, American Mathematical Society , Vol. 30 , No. 1 ,
(1971) , 43 -45 .
[7] Nakkar, H.M. Localization in multiplicative Lattice modules, (In Russia), Mat. Issledovanija, Kishinev, 2(33)
, (1974), 88-108 .
[8] Nakkar, H. M. AL-Khouja, E. A., A Locally Noetherian Lattice Modules. Tamkang Journal of Mathematics.
Volume 22, Number 3, Autumn (1991), 253- 257.
[9]. Merkepci, M,; Sarkis, M. An Application of Pythagorean Circles in Cryptography and Some Ideas for Future
Non Classical Systems. Galoitica Journal of Mathematical Structures and Applications 2022, 2, 28-30, doi:
10.54216/GJMSA.020205.
[10] Merkepci, M., and Ali, R., " A Study of Some Neutrosophic Algebraic Games and Their Winning
Stratigies", Galoitica Journal Of Mathematical Structure And Applications, Vol.2, 2022.
