For a semigroup S (group G) we study relational equations and describe all semigroups with equationally Noetherian direct powers. It follows that any group G has powers if consider as an algebraic structure of certain language. Further specify the results follows: power finite is Noetherian, then minimal ideal Ker(S) rectangular band groups coincides set reducible elements

We characterize left Noetherian rings which have only trivial derivations.

let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigate some properties of formal local cohomology modules with respect to a serre subcategory. we provide a common language to indicate some properties of formal local cohomology modules. let ( r,m ) be a noetherian local ring, a an ideal of r and m a finitely generated r- module. we investigat...