ALGEBRAIC STRUCTURE ON THE SET BASED ON ABO BLOOD TYPE

• Main Author: Constantine, Chantika
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/82341
• Institution: Institut Teknologi Bandung

Algebra, a fundamental branch of mathematics, plays a critical role in solving practical problems and serves as the foundation for the development of various other fields. In this thesis, the algebraic structure of a set built upon the ABO blood type system will be examined. The set formed based on the ABO blood type will be considered as a vector space over the field of real numbers. In the process of forming the algebra, a multiplication operation is defined, which differs from the usual multiplication operation in a vector space over the field of real numbers. The multiplication operation in this blood type algebra can be viewed as the crossing of blood types from two individuals, reflecting the possible blood types of the offspring resulting from the mating of these two individuals. The resulting algebraic structure is called the Generalized ABO-Blood Type Algebra (GBTA) and is denoted by B(?, ?). In the development of the study, another basis of the GBTA algebra is also proposed, which can simplify the multiplication operation between elements. Along with this new basis, the GBTA algebra will be denoted as B(?, ?). As a result of further analysis, several properties of the formed algebra are also examined, related to the concepts of absolute nilpotent, idempotent elements, ideals of various dimensions, and algebra isomorphism in GBTA.