Overview
- Provides a crisp review of fuzzy set theory, Lie algebras, and Lie superalgebras
- Presents the properties of interval-valued fuzzy Lie ideals, Noetherian Lie algebras, quotient Lie algebras, and interval-valued fuzzy Lie superalgebras
- Characterizes the Artinian and Noetherian Lie algebras by considering their fuzzy Lie ideals over a fuzzy field
- Discusses the concepts of m-polar fuzzy Lie subalgebras and m-polar fuzzy Lie ideals
Part of the book series: Infosys Science Foundation Series (ISFS)
Part of the book sub series: Infosys Science Foundation Series in Mathematical Sciences (ISFM)
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Table of contents (10 chapters)
Keywords
About this book
Divided into 10 chapters, the book begins with a concise review of fuzzy set theory, Lie algebras and Lie superalgebras. In turn, Chap. 2 discusses several properties of concepts like interval-valued fuzzy Lie ideals, characterizations of Noetherian Lie algebras, quotient Lie algebras via interval-valued fuzzy Lie ideals, and interval-valued fuzzy Lie superalgebras. Chaps. 3 and 4 focus on various concepts of fuzzy Lie algebras, while Chap. 5 presents the concept of fuzzy Lie ideals of a Lie algebra over a fuzzy field. Chapter 6 is devoted to the properties of bipolar fuzzy Lie ideals, bipolar fuzzy Lie subsuperalgebras, bipolar fuzzy bracket product, solvable bipolar fuzzy Lie ideals and nilpotent bipolar fuzzy Lie ideals. Chap. 7 deals with the properties of m-polar fuzzy Lie subalgebras and m-polar fuzzy Lie ideals, while Chap. 8 addresses concepts like soft intersection Lie algebras and fuzzy soft Lie algebras. Chap. 9 deals with rough fuzzy Lie subalgebras and rough fuzzy Lie ideals, and lastly, Chap. 10 investigates certain properties of fuzzy subalgebras and ideals of n-ary Lie algebras.
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Fuzzy Lie Algebras
Authors: Muhammad Akram
Series Title: Infosys Science Foundation Series
DOI: https://doi.org/10.1007/978-981-13-3221-0
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-3220-3Published: 14 January 2019
eBook ISBN: 978-981-13-3221-0Published: 30 December 2018
Series ISSN: 2363-6149
Series E-ISSN: 2363-6157
Edition Number: 1
Number of Pages: XIX, 302
Number of Illustrations: 10 b/w illustrations, 4 illustrations in colour
Topics: General Algebraic Systems, Mathematical Logic and Foundations