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Subdirectly irreducible non-idempotent left symmetric left distributive groupoids. (English) Zbl 1102.20045

Summary: We study groupoids satisfying the identities \(x\cdot xy=y\) and \(x\cdot yz=xy\cdot xz\). Particularly, we focus our attention at subdirectly irreducible ones, find a description and characterize small ones.

MSC:

20N02 Sets with a single binary operation (groupoids)
08B20 Free algebras
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