In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly module. Then every finitely M-generated module is supplemented. R any ring. if only generated R-module an e-supplement submodule in

Let M be a module over the commutative ring R. In this paper we introduce two new notions, namely strongly coprimal and super coprimal modules. Denote by ZR(M) the set of all zero-divisors of R on M . M is said to be strongly coprimal (resp. super coprimal) if for arbitrary a, b ∈ ZR(M) (resp. every finite subset F of ZR(M)) the annihilator of {a, b} (resp. F ) in M is non-zero. In this paper w...

The cardinality of the minimal generating set of a module M i.e g(M) plays a very important role in the study of QTAG-Modules. Fuchs [1] mentioned the importance of upper and lower basic subgroups of primary groups. A need was felt to generalize these concepts for modules. An upper basic submodule B of a QTAG-Module M reveals much more information about the structure of M . We find that each ba...

primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. in fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly.  in this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pr...

Consider a bounded strongly pseudo-convex domain Ω with smooth boundary in Cn. Let T be the Toeplitz algebra on Bergman space La2(Ω). That is, is C⁎-algebra generated by operators {Tf:f∈L∞(Ω)}. Extending work [27], [28] special case of unit ball, we show that any such Ω, and {Tf:f∈VObdd}+K are essential commutants each other, where K collection compact On general considered this paper, proofs r...

The notion of the square submodule of a module M over an arbitrary commutative ring R, which is denoted by RM, was introduced by Aghdam and Najafizadeh in [3]. In fact, RM is the R−submodule of M generated by the images of all bilinear maps on M. Furthermore, given a submodule N of an R−module M, we say that M is nil modulo N if μ(M×M) ≤ N for all bilinear maps μ on M. The main question about t...

Suppose that is an innnite set and k is a natural number. Let ] k denote the set of all k-subsets of and let F be a eld. In this paper we study the FSym(()-submodule structure of the permutation module F] k. Using the representation theory of nite symmetric groups, we show that every submodule of F] k can be written as an intersection of kernels of certain FSym(()-homomorphisms F] k ?! F] l for...

Submodule construction is the problem of finding a new submodule which, together with a given submodule, provides a behavior that conforms to a given desired global behavior. A new formulation of this problem and its solution in first-order logic is presented, and it is shown how the known solutions to this problem in the context of various communication paradigms and specification formalisms c...

An R-module A is called GF-regular if, for each a ∈ A and r ∈ R, there exist t ∈ R and a positive integer n such that r(n)tr(n)a = r(n)a. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by M GF(A). Furthermore, the radical properties of A are investigated; we proved that if A is an R-module and K is a submodule of A, then MGF(K) = K∩M GF(A...