Regular semigroup

A regular semigroup is like playing with blocks that only fit together in one direction.

You know how sometimes when you play with blocks, they can fit together in different ways? Well, in a regular semigroup, the blocks can only fit together one way.

Imagine you have a block with a certain pattern on it. If you try to fit that block with another block that has the same pattern, it will fit perfectly. But if you try to fit it with a block that has a different pattern, it won't fit at all.

That's kind of what a regular semigroup is like. The blocks are the different elements in the semigroup, and they can only fit together with certain other elements.

But what makes it "regular" is that every element in the semigroup can fit with at least one other element, and they all have certain properties that make them work together in this regular way.

So basically, a regular semigroup is a set of elements that can only fit together in a certain way, like blocks with specific patterns that only fit with other blocks that have the same pattern.