The boolean-rings tag has no usage guidance.

**3**

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**1**answer

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### existence of more distributive Boolean lattices

Are there a Boolean lattice $(X,\le)$ and a nonempty collection $(a_{ij})_{i\in I,j\in J}\subseteq X$ such that
$$\bigvee_{i\in I}\bigwedge_{j\in J}{a_{ij}}\ne \bigwedge_{f:I\to J}\bigvee_{i\in ...

**5**

votes

**2**answers

679 views

### 0-dimensional locally compact space

What is an example of a 0-dimensional locally compact Hausdorff space X for which the Cech-Stone compactification beta(X) is NOT 0-dimensional?
It is known that if X is a 0-dimensional locally ...

**3**

votes

**2**answers

189 views

### Chain of ideals in a BA

Suppose $\mathfrak{A}$ is a Boolean algebra and $\mathfrak{J}$ is chain of ideals in $\mathfrak{A}$ ordered by inclusion such that none of its elements is countably generated. Clearly, the union ...

**11**

votes

**4**answers

960 views

### Jonsson Boolean algebras?

Let us say that a mathematical structure of cardinality $\omega_1$ is Jonsson whenever every one of its proper substructures is countable.
There are examples of Jonsson groups due to Shelah or ...

**1**

vote

**1**answer

245 views

### References for Sheaves of Boolean Rings

I have been looking for references on sheaves that take value in the category of Boolean rings (e.g. about cohomology, etc). Would someone be able to give me some?
Or are they interesting at all? ...

**2**

votes

**3**answers

213 views

### An algebra constructed from symmetric differences

Let $S$ be a finite set. Let $R$ be a complex vector space with basis indexed by subsets of $S$. Define a product on $R$ by defining it on the basis elements as $1_A\cdot 1_B=1_{A\Delta B}$, where ...

**2**

votes

**0**answers

179 views

### relative Stone duality

Let $A$ be a fixed boolean ring. Is there a sort of classification of boolean rings $B$ with $A \subseteq B$? For example, if $A=\mathbb{F}_2$, the answer would be Stone duality: ...