Lattice of full soft Lie algebra
Subject Areas : Statistics
A. Akbar Estaji
1
(Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.)
H. Eghdami
2
(Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran.)
T. Haghdadi
3
(1) Faculty of Mathematical Science and Statistics, University of Birjand, Birjand, Iran.
2) Faculty of Basic Siences, Birjand University of Technology, Birjand, Iran)
Keywords: مشبکه, جبر لی, اتم, مشبکه فشرده,
Abstract :
In this paper, we study the relation between the soft sets and soft Lie algebras with the lattice theory. We introduce the concepts of the lattice of soft sets, full soft sets and soft Lie algebras and next, we verify some properties of them. We prove that the lattice of the soft sets on a fixed parameter set is isomorphic to the power set of a set with respect to set inclusion. In particular, we characterize the atoms in the lattice of the soft sets and the lattice of full soft Lie algebras. After that, we introduce the compact elements in the full soft Lie algebras and we present the necessary and sufficient conditions for the compactness and atomicness of the lattice of full soft Lie algebras. We show that if a full soft Lie algebra is a compact element of the lattice of full soft Lie algebra then the parameter set is finite and the Lie algebra is finitely generated. In the sequel, we study the relationship between prime and maximal ideals in Lie algebras and the prime and maximal elements in the lattice of soft Lie algebras.
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