(adsbygoogle = window.adsbygoogle || []).push({}); "simple" magmas?

I gather the modern term for a set with a closed binary operation is "magma" and that the old term "groupoid" now applies to something in category theory.

Is there a standard definition for a "simple" magma? For example, I think its straighforward to define the direct product of two finite magmas. So one thought is that a finite magma could be called "simple" if it is not isomorphic to the direct product of two smaller magmas.

(An amusing obstacle to looking up facts about magmas on the web is that the computer algebra software called Magma is the subject of so many links.)

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# Simple magmas?

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