A cohomological support, Supp A (M), is defined for finitely generated modules M over a left noetherian ring R, with respect to a ring A of central cohomology operations on the derived category of R-modules. It is proved that if the A-module Ext R (M, M) is noetherian and Ext R (M, R) = 0 for i ≫ 0, then every closed subset of Supp A (M) is the support of some finitely generated R-module. This ...

The Noetherian type of a space is the least κ such that it has a base that is κ-like with respect to reverse inclusion. Just as all known homogeneous compacta have cellularity at most c, they satisfy similar upper bounds in terms of Noetherian type and related cardinal functions. We prove these and many other results about these cardinal functions. For example, every homogeneous dyadic compactu...

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

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

We characterize left Noetherian rings which have only trivial derivations.