Characteristic of Near Ring From Group Object of Categories

N P Puspita, Titi Udjiani SRRM, S Suryoto, B Irawanto

Abstract


Setiap objek pada kategori dengan objek terminal dan produk disebut grup objek jika memiliki beberapa aksioma seperti aksioma grup tetapi didefinisikan oleh diagram komutatif. Aksioma-aksioma tersebut seperti asosiatif, eksistensi elemen identitas dan elemen invers. Untuk setiap objek kelompok G, himpunan endomorfisme dari G ke G dilambangkan dengan Hom (G, G). Hom (G, G) berada tepat di dekat ring pada opersai penjumlahan dan operasi perkalian . Dalam penelitian ini kami menunjukkan bahwa Hom (G, G) dapat dipertimbangkan sebagai cincin B1 di dekat kedua operasi tersebut.

Every object on category with terminal object and product is called group object if its have some axioms like group axioms but defined by comutative diagram. Its axioms such as associative, existence identity element and invers element. For any group object G, set of endomorphism from G to G denoted by Hom(G,G). Hom(G,G) is right near ring over addition operation and multiplication operation . In this research we shown that Hom(G,G) can be considering as B1- near ring over both operation.


Keywords


category; group object; near ring, B1- near ring

Full Text:

PDF

References


Adamek J, Herrlich H & Strectker GE. 2004. Abstract and Concrete Categories : The joy of Cats. Boston : Free Software Foundation.

Ashraf M & Siddeeque MA. 2015. On Semigroup Ideals and Generalized n Derivation in Near Rings, Sarajevo Journal Of Mathematics 11(24): 155-164 DOI: 10.5644/SJM.11.2.02

Balakhrisnam R, Silviya S & Chelvam TT. 2011. B1 near-ring, International Journal of Algebra 5(5): 199-205.

Boua A. 2012. Some Condition under which prime Near-Rings are Commutative Rings, International Journal Open Problems Compt. Math. 5(2): 7-15 DOI: 10.12816/0006101

Clay JR. 1994. Some Applications of Near rings, Rings and Radicals, Proceedings of the Internationals Conferencee, Shijiazhuang.

Fraleigh J. 1994. A first Course in Abstract Algebra. Addison - Wesley Publishing Company, Singapore.

Pareigis B. 1970. Categories and Functors, New York : Academic Press.

Pilz G. 1983. Near-ring: The Theory and its Application, North Holland, Amsterdam.

Puspita NP. 2007.Pembentukan Near Ring dari Obyek Grup dan Kogrup suatu Kategori [Skripsi]. Yogyakarta: Gadjah Mada University.

Schubert H. 1972. Categories, New York : Springer Verlag, Berlin, Heidelberg.

Silviya S, Balakhrishnan R & Chelvam TT. 2010. Strong S1 near ring. International Journal of Algebra 4(14): 685-691.


Refbacks

  • There are currently no refbacks.