Weak radical classes

Abstract

We introduce the concept of weak radical classes and proceed to construct these classes. In section 2 we define strongly austere semimodules. Theorem 1 characterizes strongly autere semimodules with respect to modular maximal subtractive ideals. We present an example of a weak radical class that can be neither a semiradical class nor a radical class. In section 4 we show that the semiradical class over a certain restricted class of semirings is equivalent to the weak radical class. We also demonstrate the construction of a semiradical class over this class. Finally, we show in example 3 that a semiradical class need not to be a radical class.