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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s) under exclusive license to Università degli Studi di Ferrara 2022
- ISSN
- 0430-3202
- eISSN
- 1827-1510
- DOI
- 10.1007/s11565-022-00407-8
- Publisher site
- See Article on Publisher Site
Abstract
The main objective of this study is to introduce a neutrosophic N-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {N}}-$$\end{document} subalgebra (ideal) of L-algebras and to investigate some properties. It is shown that the level-set of a neutrosophic N-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {N}}-$$\end{document}subalgebra (ideal) of an L-algebra is its subalgebra (ideal), and the family of all neutrosophic N-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {N}}-$$\end{document}subalgebras of an L-algebra forms a complete distributive modular lattice. Additionally, it is proved that every neutrosophic N-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {N}}-$$\end{document}ideal of an L-algebra is the neutrosophic N-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {N}}-$$\end{document}subalgebra but the inverse of the statement may not be true in general. As the concluding part, some special cases are provided as ideals which are particular subsets of an L-algebra defined due to N-\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathcal {N}}-$$\end{document}functions.
Journal
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: May 1, 2023
Keywords: L-algebra; Ideal; Neutrosophic N-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {N}}-$$\end{document}subalgebra; Neutrosophic N-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {N}}-$$\end{document}ideal; 06F05; 03G25; 03G10