Conditional complements of sets and their application to group theory

Yıl 2021, , 67 - 74, 31.12.2021

Naim Çağman

https://doi.org/10.54187/jnrs.1003890

Cited By: 8

Öz

Among the most important concepts of mathematics are sets, of which one of the critical concepts is the complement of a set. This work defines two conditional complements of sets as a new concept of set theory, i.e., inclusive complement and exclusive complement. By comparing these two, we then explore the relationships between them. We also apply them to the group theory and define complement subgroup of a group. Finally, we conclude the study with two interesting questions about the subject.

Anahtar Kelimeler

Complement of a set, Conditional complements, Inclusive complement, Exclusive complement, Complement subgroup

Kaynakça

• P. R. Halmos, Naive set theory, D. Van Nostrand Company, Inc., New York, 2011.
• J. Ferreirós, Labyrinth of thought: A history of set theory and its role in modern mathematics, Birkhäuser, Basel, 2007.
• D. S. Dummit, R. M. Foote, Abstract algebra,Wiley, Hoboken, NJ, 2004.
• T. Hungerford, Algebra, Springer, New York, 2003.