Soft Ideals Research Articles

Applications of soft sets in ideal theory of BCK/BCI-algebras

The notion of soft ideals and idealistic soft BCK/BCI-algebras is introduced, and several examples are given. Relations between soft BCK/BCI-algebras and idealistic soft BCK/BCI-algebras are provided. The intersection, union, “AND” operation, and “OR” operation of soft ideals and idealistic soft BCK/BCI-algebras are established.

Soft Ideals and Arithmetic Mean Ideals

This article investigates the soft-interior (se) and the soft-cover (sc) of operator ideals. These operations, and especially the first one, have been widely used before, but making their role explicit and analyzing their interplay with the arithmetic mean operations is essential for the study in [10] of the multiplicity of traces. Many classical ideals are ‘soft’, i.e., coincide with their soft interior or with their soft cover, and many ideal constructions yield soft ideals. Arithmetic mean (am) operations were proven to be intrinsic to the theory of operator ideals in [6, 7] and arithmetic mean operations at infinity (am-∞) were studied in [10]. Here we focus on the commutation relations between these operations and soft operations. In the process we characterize the am-interior and the am-∞ interior of an ideal.