EMIS ELibM Electronic Journals
Vol. 37(51), pp. 33--36 (1985)

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On algebras all of whose subalgebras are simple; some solutions of Plonka's problem

Sin-Min Lee

Department of Mathematics, Stevens Institute of Technology, Hoboken, New Jersey 07030, USA

Abstract: 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 non-associative rings is indicated.

Classification (MSC2000): 20L05; 17E05

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Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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