This book presents a unified course in BE-algebras with a comprehensive introduction, general theoretical basis and several examples. It introduces the general theoretical basis of BE-algebras, adopting a credible style to offer students a conceptual understanding of the subject. BE-algebras are important tools for certain investigations in algebraic logic, because they can be considered as fragments of any propositional logic containing a logical connective implication and the constant "1", which is considered as the logical value “true”.
Primarily aimed at graduate and postgraduate students of mathematics, it also helps researchers and mathematicians to build a strong foundation in applied abstract algebra. Presenting insights into some of the abstract thinking that constitutes modern abstract algebra, it provides a transition from elementary topics to advanced topics in BE-algebras. With abundant examples and exercises arranged after each section, it offers readers a comprehensive, easy-to-follow introduction to this field.
|Edition description:||1st ed. 2018|
|Product dimensions:||6.10(w) x 9.25(h) x (d)|
About the Author
SAMBASIVA RAO MUKKAMALA, a gold medalist, is an associate professor at Maharaj Vijayaram Gajapathi Raj (MVGR) College of Engineering, Andhra Pradesh, India. Earlier, he had been associated with the Department of Information Technology, Al Musanna College of Technology, Sultanate of Oman. He received his PhD degree in Mathematics from Andhra University, India, in 2009. He is an active member of the World Academic–Industry Research Collaboration Organization (WAIRCO) and the Andhra Pradesh Akademi of Sciences (APAS). With over 20 years of teaching experience, he has published two books and over 55 research papers. His areas of research are lattice theory, C-algebras, BE-algebras and implication algebras. He has delivered invited talks on his research of interest in several countries.
Table of ContentsChapter 1. Introduction.- Chapter 2. Preliminaries.- Chapter 3. Some concepts of BE-algebras.- Chapter 4. Filters of BE-algebras.- Chapter 5. Quasi-filters of BE-algebras.- Chapter 6. Prime filters of BE-algebras.- Chapter 7. Pseudo-complements.- Chapter 8. Stabilizers.- Chapter 9. States on BE-algebras.- Chapter 10. State BE-algebras.- Chapter 11. Self-maps of BE-algebras.- Chapter 12. Endomorphisms.- Chapter 13. Fuzzification of filters.- Chapter 14. Implicative filters.- Chapter 15. Positive implicative filters.- Chapter 16. Transitive filters.