Anti Soft Rings and Anti Soft Ideals in Rings

In this paper, we define the notions of anti soft subrings and anti soft ideals of a ring, with several illustrating interesting examples. Next we define the union, direct product and sum of them and we obtain some results about them. Also we consider the relationship between them and subrings and ideals of rings. Finally, we prove that image and pre image of them under ring homomorphisms are also anti soft rings and anti soft ideals, respectively