Abstract
In this paper, we define the concepts of the radical of an ideal and a primary ideal in posets. Further, the analogue of the first and the second uniqueness theorems regarding primary decomposition of an ideal are obtained. In the last section, we prove that if an ideal in a poset Q has a minimal primary decomposition, then the diameter of the corresponding zero-divisor graph with respect to this ideal is exactly equal to three.
References
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Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- Radius, Diameter and the Degree Sequence of a Graph
- On Primary Ideals in Posets
- Characterization of the Set of Regular Elements in Ordered Semigroups
- Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
- A Result Concerning Additive Mappings in Semiprime Rings
- Characterizing Jordan Derivations of Matrix Rings Through Zero Products
- Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
- The Radon-Nikodym Property and the Limit Average Range
- A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
- On Booth Lemniscate and Hadamard Product of Analytic Functions
- Recursion Formulas for Srivastava Hypergeometric Functions
- Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
- Singular Degenerate Differential Operators and Applications
- The Interior Euler-Lagrange Operator in Field Theory
- On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
- The Family F of Permutations of ℕ
- Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
- On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
- Some Norm one Functions of the Volterra Operator
- Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
- Convexity in the Khalimsky Plane
- Natural Boundary Conditions in Geometric Calculus of Variations
- Exponential Inequalities for Bounded Random Variables
- Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of φ-Mixing Sequences
- Second Order Riemannian Mechanics
- Further Remarks on an Order for Quantum Observables
Articles in the same Issue
- Radius, Diameter and the Degree Sequence of a Graph
- On Primary Ideals in Posets
- Characterization of the Set of Regular Elements in Ordered Semigroups
- Tame Automorphisms with Multidegrees in the Form of Arithmetic Progressions
- A Result Concerning Additive Mappings in Semiprime Rings
- Characterizing Jordan Derivations of Matrix Rings Through Zero Products
- Existence Results for Impulsive Nonlinear Fractional Differential Equations With Nonlocal Boundary Conditions
- The Radon-Nikodym Property and the Limit Average Range
- A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting
- On Booth Lemniscate and Hadamard Product of Analytic Functions
- Recursion Formulas for Srivastava Hypergeometric Functions
- Regularly Varying Solutions of Half-Linear Diffferential Equations with Retarded and Advanced Arguments
- Singular Degenerate Differential Operators and Applications
- The Interior Euler-Lagrange Operator in Field Theory
- On Selections of Set-Valued Maps Satisfying Some Inclusions in a Single Variable
- The Family F of Permutations of ℕ
- Summation Process of Positive Linear Operators in Two-Dimensional Weighted Spaces
- On Iλ-Statistical Convergence in Locally Solid Riesz Spaces
- Some Norm one Functions of the Volterra Operator
- Some Results on Absolute Retractivity of the Fixed Points Set of KS-Multifunctions
- Convexity in the Khalimsky Plane
- Natural Boundary Conditions in Geometric Calculus of Variations
- Exponential Inequalities for Bounded Random Variables
- Precise Rates in the Law of Iterated Logarithm for the Moment Convergence of φ-Mixing Sequences
- Second Order Riemannian Mechanics
- Further Remarks on an Order for Quantum Observables