A New Metatheorem and Subdirect Product Theorem for L-Subgroups. Issue 2 (3rd April 2018)

• Record Type: Journal Article
• Authors: Ajmal, Naseem; Jahan, Iffat
• Is Part Of: Fuzzy information and engineering. Volume 10:Issue 2(2018)
• Page Start: 129
• Page End: 144
• Publication Date: 2018-04-03
• Subjects: Lattices -- groups -- normal subgroups -- L-algebra -- metatheorem -- subdirect product theorem -- L-subgroups -- L-normal subgroups; Fuzzy systems -- Periodicals; Intelligent control systems -- Periodicals; 629.89
• DOI: 10.1080/16168658.2018.1517971
• Languages: English
• ISSNs: 1616-8658

Abstract

ABSTRACT: This paper is a continuation of the work of Tom Head 'Metatheorem for deriving fuzzy theorems from crisp versions'. The concept of natural extension is introduced which is then applied in the development of a new metatheorem in L -setting, where L is a complete chain. The application of this theorem is demonstrated through the notions of generated L -subgroups and commutator L -subgroups. Moreover, a new subdirect product theorem is developed wherein it is demonstrated that for a group G, the L -subgroup lattice can be represented as a subdirect product of copies of its associated lattice of crisp subgroups. The significance of this theorem is exhibited by applying it to a characterization of generalized cyclic groups in terms of the distributivity of the lattice of L -subgroups of a group.