Vol. 37(51), pp. 3336 (1985) 

On algebras all of whose subalgebras are simple; some solutions of Plonka's problemSinMin LeeDepartment of Mathematics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USAAbstract: For each cardinal number $\alpha\geq 1$, we construct two types of grupoids $\langle X_\alpha;\circ\rangle$ and $\langle X_\alpha; *\rangle$ which are hereditarily simple and have subgrupoids of all small orded. If $\alpha\geq \aleph_0$, we show that they both admit only discrete topology to become topological grupoids. An application of the grupoid $\langle X_\alpha; *\rangle$ in the theory of nonassociative rings is indicated. Classification (MSC2000): 20L05; 17E05 Full text of the article:
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