We examine the computably enumerable (c.e.) degrees of prime models of complete atomic decidable (CAD) theories. A structure has degree d if d is the degree of its elementary diagram. We show that if a CAD theory T has a prime model of c.e. degree c, then T has a prime model of strictly lower c.e. degree b, where, in addition, b is low (b′ = 0′). This extends Csima’s result that every CAD theor...

In this paper, we study a generalization of z-ideals in the ring C(X) of continuous real valued functions on a completely regular Hausdorff space X. The notion of a weak ideal and naturally a weak z-ideal and a prime weak ideal are introduced and it turns out that they behave such as z-ideals in C(X).

In this paper, we introduce a new subclass of harmonic functions f = s + ¯ t f=s+t¯ in the open unit disk U { z ∈ C : | < 1 } U={z∈C:|z|<1} satisfying ${\text{Re}}\left[ \gamma \mathfrak{s}^{\prime }(z)+\delta z\mathfrak{s}^{\prime \prime }(z)+\left( \frac{\delta -\gamma }{2}\right) z^{2}\mathfrak{s}^{\prime }\left( z\right) -\lambda \right]>\left \vert \mathfrak{t}^{\prime z\mathfrak{t}^{\prim...

let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

Let R be a ring, and let C denote the center of R. R is said to have a prime center if whenever ab belongs to C then a belongs to C or b belongs to C. The structure of certain classes of these rings is studied, along with the relation of the notion of prime centers to commutativity. An example of a non-commutative ring with a prime center is given.