Conditions that a strongly atomic algebraic lattice is semimodular¹

Article type: Research Article

Authors: He, Peng | Wang, Xue-ping^{; *}

Affiliations: College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan, People’s Republic of China

Correspondence: [*] Corresponding author. Xue-ping Wang, College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, People’s Republic of China. Fax: +8628 84761393; E-mail: [email protected].

Note: [1] Supported by National Natural Science Foundation of China (Nos. 11171242 and 61573240).

Abstract: This paper deals with strongly atomic algebraic lattices. Two necessary and sufficient conditions that a strongly atomic algebraic lattice is semimodular are shown by using the locally sublattice, called a WAGC sublattice, of the lattice.

Keywords: Strongly atomic lattice, algebraic lattice, semimodular lattice, WAGC lattice

DOI: 10.3233/JIFS-162168

Journal: Journal of Intelligent & Fuzzy Systems, vol. 33, no. 2, pp. 913-920, 2017