Struktur Dan Sifat-sifat K-Aljabar

Abstract

K-Algebra is constructed on a group using binary operations ⊙ on (G,*), so for each x,y∈G defined as x⊙y=x*y^(-1)=xy^(-1) with certain axioms on K-Algebra. K-Group summation is defined as the elements of K that operate summation in K, similar to addition in K itself. Meanwhile, the K-Ring has two basic operations, namely addition and multiplication, both of which must satisfy certain properties and use the K-Field as a scalar field. Finally, the K-Field is described as a special K-Algebra structure in which the multiplication operation is distributive to the addition operation. This research contributes to a deeper understanding of structures and operations in K-Algebra. The next research is that K-Algebra can be applied in sets meaning that it can be applied to sets of numbers, dihedral, and modulo or congruence, which are equipped with theorems, proofs, and examples.