GDL

Journal from gdlhub / 2019-05-20 14:19:06
Oleh : Naseem Ajmal & Iffat Jahan, Fuzzy Information and Engineering
Dibuat : 2019-05-20, dengan 1 file

Keyword : Lattices, groups, normal subgroups, L-algebra, metatheorem, subdirect product theorem, L-subgroups, L-normal subgroups
Url : http://www.tandfonline.com/doi/full/10.1080/16168658.2018.1517971
Sumber pengambilan dokumen : WEB

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.

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