This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w.r.t. {+, −, ×, >, ≥} in a constructive setting. Introduction This paper is a survey of natural questions (with few answers) arising when one wants to study algebraic properties of real numbers, i.e., properties of real numbers w....

¡v in this paper we consider a strongly regular relation ƒá on hypermodules so that the quotient is amodule (with abelian group) over a fundamental commutative ring. also, we state necessary and sufficientconditions so that the relation ƒá is transitive, and finally we prove that ƒá is transitive on hypermodules.

The algorithms for linear algebra in the Magma and Axiom computer algebra systems work over an arbitrary ring. For example, the implementation of Gaussian elimination for reducing a matrix to (reduced) row Echelon form works over any field that the user constructs. In contrast, Maple’s facilities for linear algebra in its LinearAlgebra package only work for specific rings. If the input matrix c...

The notion of a weak multiresolution analysis is defined over an arbitrary field in terms of cyclic modules for a certain affine group ring. In this setting the basic properties of weak multiresolution analyses are established, including characterizations of their submodules and quotient modules, the existence and uniqueness of reduced scaling equations, and the existence of wavelet bases. Thes...

An efficient and simple method for the preparation of Si-Imidazole-HSO4 functionalized magnetic Fe3O4 nanoparticles (Si-Im-HSO4 MNPs) and used as an efficient and reusable magnetic catalysts for the regioselective ring opening of epoxides under green conditions in water. This catalyst was used for the ring opening of epoxide corresponding to the thiocyanohydrins and azidohydrines. Compared to t...

The aim of this paper is to define a new kind of fuzzy gamma ring. So the concepts of fuzzy gamma ring, fuzzy ideal, fuzzy quotient gamma ring, and fuzzy gamma homomorphism are introduced.