# Characterization of ideals in L-algebras by 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}structures

Characterization of ideals in L-algebras by neutrosophic N-\documentclass[12pt]{minimal}... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ANNALI DELL UNIVERSITA DI FERRARA Springer Journals

# Characterization of ideals in L-algebras by 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}structures

, Volume 69 (1) – May 1, 2023
20 pages

/lp/springer-journals/characterization-of-ideals-in-l-algebras-by-neutrosophic-n-pO0aqFjUJw

# References (28)

Publisher
Springer Journals
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 FERRARASpringer 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