We introduce the concept of generalized fuzzy module ofBCK-algebras and present some fundamental properties. Also, we introduce the concept of generalized interval-valued fuzzyBCK-submodule and present some fundamental properties.
Let R be an associative prime ring, U a Lie ideal such that u 2 ∈U for all u∈U and F: R→R be a generalized derivation. In this paper, we show that U ⊆ Z(R) if any one of the following conditions holds: (i) F(uv) -uv∈Z(R),(ii) F(uv) -vu∈Z(R), (iii) uF(v) + uv∈Z(R), and (iv) [F(u), v] + uv∈Z(R) for all u, v∈U. If we choose the underlying subset of R as an ideal instead of a Lie ideal of R, then we prove the commutativity of prime ring.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.