Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....

By a near-ring we mean a right near-ring. J 0 , the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radical J 0 are studied. It is shown that J 0 is a Kurosh-Amitsur radical KA-radical in the variety of all near-rings R, in which the constant part Rc of R is an ideal of R. So unlike the left Jacobson radicals of ty...

Abstract Alongside the analogy between maximal ideals and complete theories, Jacobson radical carries over from of commutative rings to theories propositional calculi. This prompts a variant Lindenbaum’s Lemma that relates classical validity intuitionistic provability, syntactical counterpart which is Glivenko’s Theorem. The in fact turns out coincide with deductive closure. As by-product we ob...