Prasetyo, Puguh Wahyu and Marubayashi, Hidetoshi and Wijayanti, Indah Emilia (2022) On the restricted graded Jacobson radical of rings of Morita context. Turkish Journal of Mathematics, 46 (5). pp. 19851993. ISSN 13000098
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Abstract
Abstract: The class of rings J = {A(A, ◦) forms a group} forms a radical class and it is called the Jacobson radical
class. For any ring A, the Jacobson radical J (A) of A is defined as the largest ideal of A which belongs to J . In fact, the
Jacobson radical is one of the most important radical classes since it is used widely in another branch of abstract algebra,
for example, to construct a twosided brace. On the other hand, for every ring of Morita context T =(R V W S), we will
show directly by the structure of the Jacobson radical of rings that the Jacobson radical J (T) = (J (R) V0 W0 J (S)), where J (R) and J (S) are the Jacobson radicals of R and S , respectively, V0 = {v ∈ V vW ⊆ J (R)} and W0 = {w ∈ WwV ⊆ J (S)}. This clearly shows that the Jacobson radical is an N−radical. Furthermore, we
show that this property is also valid for the restricted G−graded Jacobson radical of graded ring of Morita context.
Item Type:  Artikel Umum 

Subjects:  Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science 
Divisi / Prodi:  Faculty of Teacher Training and Education (Fakultas Keguruan dan Ilmu Pendidikan) > S1Mathematics Education (S1Pendidikan Matematika) 
Depositing User:  puguh prasetyo 
Date Deposited:  18 Nov 2022 01:32 
Last Modified:  18 Nov 2022 01:32 
URI:  http://eprints.uad.ac.id/id/eprint/37532 
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