Let R be a commutative ring with identity , and M is unitary left R-module”, “A proper submodule E of an R-module called weakly quasi-prime if whenever r, s ∈ R, m M, 0 ≠ rsm implies that rm or sm E”. “We introduce the concept quasi 2-absorbing as generalization submodule”, where r,s,t ∈M 0≠ rstm rtm stm E. we study basic properties 2-absorbing. Furthermore, relationships other classes module a...

In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules

The profile of a relational structure R is the function φR which counts for every integer n the number, possibly infinite, φR(n) of substructures of R induced on the n-element subsets, isomorphic substructures being identified. If φR takes only finite values, this is the Hilbert function of a graded algebra associated with R, the age algebra K.A(R), introduced by P. J. Cameron. In this paper, w...

The profile of a relational structure R is the function φR which counts for every integer n the number φR(n), possibly infinite, of substructures of R induced on the n-element subsets, isomorphic substructures being identified. If φR takes only finite values, this is the Hilbert function of a graded algebra associated with R, the age algebra KA(R), introduced by P. J. Cameron. In this paper we ...

Using the general notion of distance function introduced in [2], a construction of the finest distance structure (d, M, P ) that induces a given quasiuniformity is given, which leads to a concrete, full, and co-reflective embedding of the category of quasi-uniformities into that of distance spaces. Moreover, when the usual defining condition xUεy :⇔ d(y, x) 6 ε of the basic entourages is genera...

We present here a quite unexpected result: Apart from already known commutative C∗-algebras generated by Toeplitz operators on the unit ball, there are many other Banach algebras generated by Toeplitz operators which are commutative on each weighted Bergman space. These last algebras are non conjugated via biholomorphisms of the unit ball, non of them is a C∗-algebra, and for n = 1 all of them ...

Building upon work of Y. Shalom we give a homological-algebra flavored definition of an induction map in group homology associated to a topological coupling. As an application we obtain that the cohomological dimension cdR over a commutative ring R satisfies the inequality cdR(Λ) ≤ cdR(Γ) if Λ embeds uniformly into Γ and cdR(Λ) < ∞ holds. Another consequence of our results is that the Hirsch ra...

We describe new Banach (not C∗ !) algebras generated by Toeplitz operators which are commutative on each weighted Bergman space over the unit ball B, where n > 2. For n = 2 all these algebras collapse to the single C∗-algebra generated by Toeplitz operators with quasi-parabolic symbols. As a by-product, we describe the situations when the product of mutually commuting Toeplitz operators is a To...

We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent algebraic characterisations are provided. It is shown that in characteristic zero the corresponding generic positions can be obtained with a simple deterministic al...