Every Integral Domain Artinian Ring is a Field
Problem 437
Let $R$ be a ring with $1$. Suppose that $R$ is an integral domain and an Artinian ring.
Prove that $R$ is a field.
Add to solve later Tagged: Artinian
Add to solve later Add to solve later This website’s goal is to encourage people to enjoy Mathematics!
This website is no longer maintained by Yu. ST is the new administrator.
Linear Algebra Problems by Topics
Subscribe to Blog via Email
Sponsored Links
Sponsored Links
Categories
- Elementary Number Theory (1)
- Field Theory (27)
- General (7)
- Group Theory (126)
- Linear Algebra (485)
- Math-Magic (1)
- Module Theory (13)
- Probability (33)
- Ring theory (67)
- Welcome (1)
MathJax
Mathematical equations are created by MathJax.
See How to use MathJax in WordPress if you want to write a mathematical blog.
Recent Posts
- How to Prove Markov’s Inequality and Chebyshev’s Inequality
- How to Use the Z-table to Compute Probabilities of Non-Standard Normal Distributions
- Expected Value and Variance of Exponential Random Variable
- Condition that a Function Be a Probability Density Function
- Conditional Probability When the Sum of Two Geometric Random Variables Are Known
Sponsored Links
Top Posts
- How to Diagonalize a Matrix. Step by Step Explanation.
- Determine Whether Each Set is a Basis for $\R^3$
- Express a Vector as a Linear Combination of Other Vectors
- How to Find a Basis for the Nullspace, Row Space, and Range of a Matrix
- The Intersection of Two Subspaces is also a Subspace
- Prove that $\{ 1 , 1 + x , (1 + x)^2 \}$ is a Basis for the Vector Space of Polynomials of Degree $2$ or Less
- Rank of the Product of Matrices $AB$ is Less than or Equal to the Rank of $A$
- Show the Subset of the Vector Space of Polynomials is a Subspace and Find its Basis
- 12 Examples of Subsets that Are Not Subspaces of Vector Spaces
- Find a Basis and the Dimension of the Subspace of the 4-Dimensional Vector Space