Abstract
In this paper, the notion of the soft Jacobson radical of a ring is defined. A relationship between the soft Jacobson radical of a ring and Jacobson semisimple ring is established. Some properties of this notion have been studied under homomorphism.
Highlights
The idea of a soft set was introduced by D
Algebraic structure in soft set theory was introduced by Aktas and Cagman [2] in 2007
They defined a soft group as a parametrized family of subgroups of the given group
Summary
The idea of a soft set was introduced by D. Algebraic structure in soft set theory was introduced by Aktas and Cagman [2] in 2007. They defined a soft group as a parametrized family of subgroups of the given group. Extending the notion of a soft group, several algebraic structures like soft ring [1], soft ideal [6], soft vector space [15] etc., have been introduced. In 2012, Cagman et al [5] defined group structure on a soft set in a new way using set inclusion relation. This concept has been named as soft int-group. If f is an epimorphism from a ring R to a ring R , we prove that the homomorphic pre-image of the soft Jacobson radical of R is equal to the soft Jacobson radical of R under a suitable condition
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