# Category:Subrings

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This category contains results about Subrings.

Let $\struct {R, +, \circ}$ be an algebraic structure with two operations.

A **subring of $\struct {R, +, \circ}$** is a subset $S$ of $R$ such that $\struct {S, +_S, \circ_S}$ is a ring.

## Subcategories

This category has the following 4 subcategories, out of 4 total.

### D

### I

### R

### S

## Pages in category "Subrings"

The following 38 pages are in this category, out of 38 total.

### C

### I

- Image of Preimage of Ideal under Ring Epimorphism
- Image of Preimage of Subring under Ring Epimorphism
- Increasing Union of Subrings is Subring
- Integers form Subring of Reals
- Intersection of Subrings Containing Subset is Smallest
- Intersection of Subrings is Largest Subring Contained in all Subrings
- Intersection of Subrings is Subring
- Inverse of Central Unit of Ring is in Center
- Inverse of Unit in Centralizer of Ring is in Centralizer

### P

### R

### S

- Set of Polynomials over Integral Domain is Subring
- Set of Subrings forms Complete Lattice
- Subdomain Test
- Subring Module
- Subring Module/Special Case
- Subring of Integers is Ideal
- Subring of Polynomials over Integral Domain Contains that Domain
- Subring of Polynomials over Integral Domain is Smallest Subring containing Element and Domain
- Subring Test
- Subrings of Integers are Sets of Integer Multiples
- Sum of Ring Products is Subring of Commutative Ring