Abstract:
A ring A is called presimplifiable if whenever a; b belongs to A and a = ab, then either a = 0 or b is a unit in A. Let A be a commutative ring and G be an abelian torsion group. For the group ring A[G], we prove that A[G] is presimplifiable if and only if A is presimplifiable and G is a p-group with p belongs to the Jacobson radical of A, and it is shown that A[G] is domainlike (i.e all zero divisors are nilpotents) if and only if A is domainlike and G is a p-group and p is a nilpotent in A. Furthermore, whenever the group ring A[G] is presimpli?able we prove that A[H] is presimplifiable for any subgroup H of G. Also, for a torsion free group G we prove that A[G] is domainlike if and only if A[G] is integral domain.

Abstract:
We develop basic notions and methods of algebraic geometry over the algebraic objects called hyperrings. Roughly speaking, hyperrings generalize rings in such a way that an addition is `multi-valued'. This paper largely consisits of two parts; algebraic aspects and geometric aspects of hyperrings. We first investigate several technical algebraic properties of a hyperring. In the second part, we begin by giving another interpretation of a tropical variety as an algebraic set over the hyperfield which canonically arises from a totally ordered semifield. Then we define a notion of an integral hyperring scheme $(X,\mathcal{O}_X)$ and prove that $\Gamma(X,\mathcal{O}_X)\simeq R$ for any integral affine hyperring scheme $X=Spec R$.

Abstract:
Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x+y of two elements, x,y, of a hyperring H is, in general, not an element but a subset of H. When the non-zero elements of a hyperring form a multiplicative group, the hyperring is called a hyperfield, and this structure generalizes that of a field. A certain class of hyperfields (residual hyperfields of valued fields) has been used by the author [1] as an important technical tool in his theory of approximation of complete valued fields by sequences of such fields. Tne non-commutative theory of hyperrings (particularly Artinian) has been studied in depth by Stratigopoulos [2].

Abstract:
The concept of normal fuzzy hyperideals of hyperrings is introduced and then some fuzzy isomorphism theorems of hyperrings is obtained by normal fuzzy hyperideals.

Abstract:
We consider minimal immersions in MxR. We study existence and uniqueness of associate and conjugate isometric immersions to a given minimal surface. We use the theory of univalent harmonic map between surfaces. Then we study the geometry of associate minimal vertical graphs. We prove that an associate surface of a vertical graph on a convex domain is a graph. In the classical theory it is a theorem of R. Krust.

Abstract:
Associate learning is fundamental to the acquisition of knowledge and plays a critical role in the everyday functioning of the developing child, though the developmental course is still unclear. This study investigated the development of visual associate learning in 125 school age children using the Continuous Paired Associate Learning task. As hypothesized, younger children made more errors than older children across all memory loads and evidenced decreased learning efficiency as memory load increased. Results suggest that age-related differences in performance largely reflect continued development of executive function in the context of relatively developed memory processes.

Abstract:
I am happy to welcome the new Associate Editor-in-Chief of the JETWI, Dr. Jiehan Zhou, to the editorial board. Sabah Mohammed Editor-in-Chief August 2010