SIFAT ELEMENTER DARI RING TERGENERALISASI - Rosyadi, Gusti Muhammad; Hijriati, Na'imah (Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat, 2024)
Ring is a study of algebraic structures, which is defined as a non-empty set containing two binary operations. Regarding the first binary operation, the set is a group, and the second binary operation is a semigroup, and both operations fulfill the left distributive and right distributive properties. The generalized ring concept is an extension of the ring concept, namely that for the first binary operation, each element has an identity element that is not necessarily the same. This research aims to prove the elementary properties of generalized rings and the properties of generalized rings associated with the G-ring structure. Furthermore, this research also proves the properties of subsets related to identity elements in generalized rings. The results of this research are that the fundamental properties of the generalized ring are valid, which are analogous to the fundamental properties of the ring, and sufficient conditions for a generalized ring to be a G-ring are obtained. Furthermore, if the generalized ring has a unit element, it forms an abelian group with all elements having the same identity, and the generalized ring contains all identity elements.