关于代数结构magma的课程设置及命名疑问咨询

Hey there! I’ve never taken a formal abstract algebra course myself, but I’ve picked up a bit about how the typical curriculum is structured:

• First, define what an algebraic structure is in general
• Then explain groups in detail
• Then move on to... well, everything else that builds on groups

But it always struck me that we skip over the most fundamental algebraic structure of all: the magma

A magma is probably the simplest algebraic structure you can imagine—way simpler than groups! Here's the full, straightforward definition:

A magma is a set equipped with one binary operation which is closed by definition.

That’s literally all there is to it! No extra constraints like associativity, identity elements, or inverses—just a set and a closed binary operation.

Some super common magmas you interact with every day include:

• Integers under addition, subtraction, or multiplication
• Real numbers under addition, subtraction, multiplication, or division
• Complex numbers under all standard arithmetic operations

I’ve always wondered why magmas never came up during my self-study of groups? It feels like such a foundational piece that’s missing from the usual curriculum flow.

There’s a great diagram that maps out how magmas fit into the hierarchy of algebraic structures leading up to groups—it’s a really nice visual that clarifies how all these structures connect to each other, showing the progression from the simplest magma to more complex structures like groups.

Also, quick fun thought—I find the name "magma" totally interesting! Why does it share the same name as that molten natural material that forms igneous rocks? It adds such a mysterious, quirky vibe to this otherwise straightforward algebraic concept.

备注：内容来源于stack exchange，提问作者user1286095