Necati Olgun

A Problem on Universal Modules

The main result in this article gives a partial answer to the following question for n = 2. Let k[U] and k[V] be the coordinate rings of the irreducible algebraic sets U and V, respectively. Is projective dimension of J n (k[U × V]) finite whenever projective dimension of J n (k[U]) and projective dimension of J n (k[V]) are finite?

Fundamental Homomorphism Theorems for Neutrosophic Extended Triplet Groups

In classical group theory, homomorphism and isomorphism are significant to study the relation between two algebraic systems. Through this article, we propose neutro-homomorphism and neutro-isomorphism for the neutrosophic extended triplet group (NETG) which plays a significant role in the theory of neutrosophic triplet algebraic structures. Then, we define neutro-monomorphism, neutro-epimorphism, and neutro-automorphism. We give and prove some theorems related to these structures. Furthermore, the Fundamental homomorphism theorem for the NETG is given and some special cases are discussed. First and second neutro-isomorphism theorems are stated. Finally, by applying homomorphism theorems to neutrosophic extended triplet algebraic structures, we have examined how closely different systems are related.

Soft normed rings.

Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainty. In this paper, we initiate the study of soft normed rings by soft set theory. The notions of soft normed rings, soft normed ideals, soft complete normed rings are introduced and also several related properties and examples are given.

On the Second-Degree Exterior Derivation of Kahler Modules on X ⊗ Y

This article presents a new approach to stress the properties of Kahler modules. In this paper, we construct the Kahler modules of second-degree exterior derivations and we constitute an exact sequence of X ⊗ Y -modules. Particularly, we examine Kahler modules on X ⊗ Y , and search for the homological size of Λ 2 ( Ω 1 ( X ⊗ Y ) ) .

Generalized Caratheodory Extension Theorem on Fuzzy Measure Space

Lattice-valued fuzzy measures are lattice-valued set functions which assign the bottom element of the lattice to the empty set and the top element of the lattice to the entire universe, satisfying the additive properties and the property of monotonicity. In this paper, we use the lattice-valued fuzzy measures and outer measure definitions and generalize the Caratheodory extension theorem for lattice-valued fuzzy measures.