Abstract
Abstract One of algebraic structure that involves a binary operation is a group that is defined an un empty set (classical) with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and group of fuzzy, a research on the algebraic structure of the ring is held with reviewing ring fuzzy, ideal ring fuzzy, homomorphism ring fuzzy and quotient ring fuzzy with its properties. The results of this study are obtained fuzzy properties of the ring, ring ideal properties fuzzy, properties of fuzzy ring homomorphism and properties of fuzzy quotient ring by utilizing a subset of a subset level and strong level as well as image and pre-image homomorphism fuzzy ring. Keywords: fuzzy ring, subset level, homomorphism fuzzy ring, fuzzy quotient ring
Highlights
Algebraic structure that involves a binary operation one of which is a group that defines a set of is not empty with a binary operation is associative, have identity elements and each element has an inverse
In the structure of the group known as the term subgroup
classical algebraic structures developed by the researchers to algebraic structure
Summary
Struktur aljabar yang melibatkan satu operasi biner salah satunya adalah grup yang didefinisikan suatu himpunan (klasik) tak kosong dengan satu operasi biner bersifat asosiatif, mempunyai elemen identitas dan setiap elemennya mempunyai invers. Di dalam struktur grup dikenal istilah subgrup, subgrup normal, subgrup faktor dan homomorfisme grup serta sifat-sifatnya. A. Zadeh 1965, struktur aljabar klasik dikembangkan oleh peneliti ke struktur aljabar fuzzy sebagai contoh semigrup fuzzy dan grup fuzzy. Diinsiprasi dari tulisan mengenai semigrup fuzzy dan grup fuzzy tersebut dilakukan penelitian pada struktur aljabar ring dengan mengkaji ring fuzzy, ideal ring fuzzy, homomorfizme ring fuzzy dan ring hasil bagi fuzzy beserta sifat-sifatnya. Hasil dari kajian ini adalah diperoleh sifat dari ring fuzzy, sifat ideal ring fuzzy, sifat homomorfisme ring fuzzy dan sifat ring hasil bagi fuzzy dengan memanfaatkan subhimpunan level dan subhimpunan level kuat serta peta dan pra-peta homomorfime ring fuzzy. Kata kunci: ring fuzzy, subhimpunan level, subhimpunan level kuat, ideal ring fuzzy, homomorfisme ring fuzzy, ring hasil bagi fuzzy
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