# Eda YıldızYildiz Technical University · Department of Mathematics

Eda Yıldız

Phd Candidate

## About

22

Publications

3,973

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37

Citations

Citations since 2017

Introduction

Algebraic Coding Theory, Quantum Error Correcting Codes, Commutative Algebra

**Skills and Expertise**

Additional affiliations

January 2017 - present

Education

September 2017 - August 2023

September 2015 - May 2017

## Publications

Publications (22)

Let A be a commutative ring with nonzero identity. In this paper, we introduce the concept of (2,J)-ideal as a generalization of J-ideal. A proper ideal P of A is said to be a (2,J)-ideal if whenever abc ∈ P and a,b,c ∈ A, then ab ∈ P or ac ∈ Jac(A) or bc ∈ Jac(A). Various examples and characterizations of (2,J)-ideals are given. Also, we study man...

Let R be a commutative ring with nonzero identity and, S �
R be a multiplicatively closed subset. Recall from [22], an ideal P of R with
P \ S = ; is called an S-prime ideal if there exists an (�fixed) s 2 S and
whenver ab 2 P for a; b 2 R then either sa 2 P or sb 2 P. In this paper,
we construct a topology on the set SpecS(R) of all S-prime ideals...

In this paper, we give the exact number of \({{\mathbb {Z}}}_{2}{{\mathbb {Z}}}_{4}\)-additive cyclic codes of length \(n=r+s,\) for any positive integer r and any positive odd integer s. We will provide a formula for the the number of separable \({{\mathbb {Z}}_{2}{{\mathbb {Z}}_{4}}}\)-additive cyclic codes of length n and then a formula for the...

In this study, we construct quantum error correcting codes over Eisenstein-Jacobi integers by using the CSS code construction. Since there is an isomorphism between EisensteinJacobi integers and finite fields, direct constructions of quantum codes over Eisenstein-Jacobi integers can be obtained. Therefore, we define error bases, error matrices and...

Abstract. Let R be a commutative ring with nonzero identity and M be an R-module. In this paper, first we give some relations between S-prime and S-maximal submodules that are generalizations of prime andmaximal submodules, respectively. Then we construct a topology on the set of all S-prime submodules ofM , which is generalization of prime spectru...

In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let [Formula: see text] be a commutative ring with a nonzero identity and [Formula: see text] be a nonzero unital module. A proper submodule [Formula: see text] of [Formula: see text] is said to be a weakly 1-absorbing primary submodule if whenever...

In this article, we introduce graded strongly quasi primary ideals which is an intermediate class of graded primary ideals and graded quasi primary ideals. Let G be a group with identity e, R be a G-graded com-mutative ring with nonzero unity 1 and P be a proper graded ideal of R. Then P is said to be a graded strongly quasi primary ideal if xy ∈ P...

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let G be a group and R be a G-graded commutative ring with a nonzero identity 1 ̸ = 0. A proper graded ideal P of R is called a graded weakly 1-absorbing prime ideal if for each nonunits x, y, z ∈ h(R) with 0 ̸ = xyz ∈ P , then either xy ∈ P or...

Let $R$ be a commutative ring with nonzero identity and $n$ be a positive integer. In this paper, we introduce and investigate a new subclass of the class of $\phi$-$n$-absorbing primary ideals called $\phi$-$(n,N)$-ideals. Let $\phi:\mathfrak{I}(R)\rightarrow \mathfrak{I}(R)\cup \{\emptyset\}$ be a function where $\mathfrak{I}(R)$ denotes the
set...

Let $G$ be a group, $R$ be a $G$-graded commutative ring with nonzero unity and $GI(R)$ be the set of all graded ideals of $R$. Suppose that $\phi:GI(R)\rightarrow GI(R)\cup\{\emptyset\}$ is a function. In this article, we introduce and study the concept of graded $\phi$-$1$-absorbing prime ideals. A proper graded ideal $I$ of $R$ is called a grade...

Let G be a group with identity e, R be a commutative G-graded ring with unity 1 and M be a G-graded R-module. In this article, we introduce and study the concept of graded weakly 2-absorbing semi-primary submodules. A proper graded R-submodule N of M is said to be graded weakly 2-absorbing semi-primary if whenever r, s ∈ h(R) and m ∈ h(M) such that...

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity $1\neq 0$. A proper ideal $P$ of $A$ is said to be a weakly 1-absorbing prime ideal if for each nonunits $x, y, z \in A$ with $0\neq xyz \in P$, then either $xy \in P$ or $z \in P$. In addition to give many prop...

Let G be a group with identity e and R be a G-graded commutative ring with unity1.In this article, we introduce and study the concept of graded1 absorbing prime ideals which is a generalization of graded prime ideals. A proper graded ideal P of R is calledgraded1-absorbing prime if for all non-unit elements x, y, z \in h(R) such that xyz \in P, the...

Let G be a group with identity e and R be a G-graded commutative ring with unity 1. In this article, we introduce and study the concept of graded 1-absorbing prime ideals which is a generalization of graded prime ideals. A proper graded ideal P of R is called graded 1-absorbing prime if for all nonunit
On graded 1-absorbing prime ideals
elements x,...

In this paper, we introduce φ-1-absorbing prime ideals in commutative rings. Let R be a
commutative ring with a nonzero identity 1\neq 0 and φ:I(R)→I(R)∪{∅} be a
function where I(R) is the set of all ideals of R. A proper ideal I of R is called a φ-1-
absorbing prime ideal if for each nonunits x,y,z∈R with xyz∈I−φ(I), then either xy∈I or
z∈I. In ad...

In this paper, we introduce φ-1-absorbing prime ideals in commu-tative rings. Let R be a commutative ring with a nonzero identity 1 = 0 and φ : I(R) → I(R) ∪ {∅} be a function where I(R) is the set of all ideals of R. A proper ideal I of R is called a φ-1-absorbing prime ideal if for each nonunits x, y, z ∈ R with xyz ∈ I − φ(I), then either xy ∈ I...

This paper introduce and study weakly 1-absorbing prime ideals in commutative rings. Let $A$ be a commutative ring with a nonzero identity $1\neq 0$. A proper ideal $P$ of $A$ is said to be a weakly 1-absorbing prime ideal if for each nonunits $x, y, z \in A$ with $0\neq xyz \in P$, then either $xy \in P$ or $z \in P$. In addition to give many prop...

In this article, we introduce and study S-comultiplication module which is the dual notion of S-multiplication module.We also characterize certain class of rings-modules such as comultiplication modules,S-second submodules,S-prime ideals,S-cyclic modules in terms of S-comultiplication modules.

In this study, an identification scheme between aircraft fleets is designed to prevent any unauthorized aircrafts from introducing themselves as friends. This method can be used as a solution to the problem of identification. The method is a combination of classical cryptographic methods and zero knowledge proof. Aircrafts which belong the same fle...

There are some differences between quantum and classical error corrections [4].Hence, these differences should be considered when a new procedure is performed.In our recent study, we construct new quantum error correcting codes over different mathematical structures. The classical codes over Eisenstein-Jacobi(EJ) integers are mentioned in [3]. Ther...

Though classical computers have been developed day by day, a new machine which is based on quantum mechanics and is called quantum computer is expected more powerful than a classical one. For instance, RSA which is a powerful cryptographic algorithm in classical computers is used in recent security systems and this algorithm cannot be cracked by us...

## Questions

Questions (4)

If we have a quantum stabilizer group, then fixed space is constructed by using this group and it is called quantum stabilizer code.

Multiplication relation between Pauli matrices give some terms with "i" like that XY=iZ. But, we sometimes ignore these complex coefficients when we construct a quantum stabilizer code. So, codewords don't contain any term with "i". Why we have this case? As far as I concerned, if any error can be corrected, then "i" multiple of it can be also corrected. But if we have some cases with "i", why is it wrong?

I try to find rank of NN^T for generalization of quadrangles. But I am not sure about it. If t is odd, rank is 5 according to me. When t is even, statement is different. Is there any programme for construct these quadrangles and their matrix?

Quantum operator codes are generalization of stabilizer codes. But in here, we additionally use gauge operators. There are some construction algorithms with parameter, but there is no obvious example about contruction it except for Shor-Bacon code. Can you give a small example which explain this code to understand clearly? Like to decomposing space, finding logical and gauge operators?

What is the benefit entangled qubits in error correction? I mean that if we used arbitrary qubit instead of entangled one in entanglement assisted quantum codes, what would be different?

Namely what is the advantage of this statement?

## Projects

Projects (4)

Our main aim is that study some generalizations of prime ideals in commutative rings and characterize rings by using these generalizations.