All Questions

We have the idea of a prime ideal in a commutative ring $R$ but in universal algebra, we generalize the notion of ideal to that of a congruence. I’ve thought over the question of what a prime ...

Given an algebra $\mathbf{A}$, a pair of congruences $ \alpha ,\beta \in Con(\mathbf {A})$ are said to permute when $ \alpha \circ \beta =\beta \circ \alpha$, and an algebra $\mathbf{A}$ is called ...

By a theorem of Hagemann and Mitschke, a condition (A) that a variety $\mathcal{V}$ is congruence $n$-permutable, is equivalent to a condition (B) that there exist ternary terms $p_1,\dots,p_{n-1}$ ...

I am currently reading Arthur Ogus' "Lectures on Logarithmic Algebraic Geometry" (https://math.berkeley.edu/~ogus/preprints/log_book/logbook.pdf). I'm trying to understand why the amalgamated sum of ...

If there is no restriction on $n$, this is a famous open problem. I'm wondering if any recent work has been done for small $n>6$. I believe the question is answered (positively) for $n=6$ by ...