Smarandache fantastic ideals of Smarandache BCI-algebras

The notion of Smarandache fantastic ideals is introduced, examples are given, and related properties are investigated. Relations among Q-Smarandache fresh ideals, Q-Smarandache clean ideals and Q-Smarandache fantastic ideals are given. A characterization of a Q-Smarandache fantastic ideal is provided. The extension property for Q-Smarandache fantastic ideals is established

Soft ideals and arithmetic mean ideals

This article investigates the soft-interior and the soft-cover 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 of the multiplicity of traces (see arXiv:0707.3169v1 [math.FA]). 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 by the work of Dykema, Figiel, Weiss, and Wodzicki on the structure of commutators and arithmetic mean operations at infinity were studied in arXiv:0707.3169v1 [math.FA]. Here we focus on the commutation relations between these operations and soft operations. In the process we characterize the am-interior and the am-infinity interior of an ideal.Comment: 21 page