# Category:Algebraic Closure

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This category contains results about **Algebraic Closure**.

Definitions specific to this category can be found in Definitions/Algebraic Closure.

Let $\struct {S, \circ}$ be an algebraic structure.

Then $S$ has the property of **closure under $\circ$** if and only if:

- $\forall \tuple {x, y} \in S \times S: x \circ y \in S$

$S$ is said to be **closed under $\circ$**, or just that **$\struct {S, \circ}$ is closed**.

## Subcategories

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

## Pages in category "Algebraic Closure"

The following 29 pages are in this category, out of 29 total.

### I

### M

### N

### R

### S

- Set of Rational Numbers whose Numerator Divisible by p is Closed under Addition
- Set of Rational Numbers whose Numerator Divisible by p is Closed under Multiplication
- Strictly Positive Rational Numbers are Closed under Multiplication
- Strictly Positive Real Numbers are Closed under Division
- Strictly Positive Real Numbers are not Closed under Subtraction