The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this it is relationship to previous generalizationsm especially 2-Absorbing submodule submodule, addition studying most important Propositions, charactarizations Examples. Now research, which considered a continuation definition tha...

‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

Let F/Q be a number field closed under complex conjugation. Denote by L0(F (t)) the Witt group of hermitian forms over F (t). We find full invariants for detecting non–zero elements in L0(F (t))⊗Q, this group plays an important role in topology in the work done by Casson and Gordon. 1. L-groups and signatures Let R be a ring with (possibly trivial) involution. An –hermitian ( = ±1) form is a se...

Let G be a complex simple Lie group and let g = LieG. Let S(g) be the G-module of polynomial functions on g and let Sing g be the closed algebraic cone of singular elements in g. Let L ⊂ S(g) be the (graded) ideal defining Sing g and let 2r be the dimension of a G-orbit of a regular element in g. Then Lk = 0 for any k < r. On the other hand, there exists a remarkable G-module M ⊂ Lr which alrea...

‎Let $R$ be commutative ring with identity and $M$ be an $R$-module‎. ‎The zero divisor graph of $M$ is denoted $Gamma{(M)}$‎. ‎In this study‎, ‎we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M‎, ‎N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$‎. ‎The main objective of this pa...

The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.

Let φ be a Drinfeld module of generic characteristic, and let X be a sufficiently generic affine subvariety of Ga. We show that the intersection of X with a finite rank φ-submodule of Ga is finite. Mathematics Subject Classification Number: Primary 11G09; Secondary 11G10.