EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 38(52), pp. 65--68 (1985)

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ON FINITE-ELEMENT SIMPLE EXTENSIONS OF A COUNTABLE COLLECTION OF COUNTABLE GROUPOIDS

Sin-Min Lee

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

Abstract: Belkin and Gorbunov [2] showed that any two finite groupoids can be imbedded into a finite simple groupoid. We prove here a stronger result: Any countable collection $\{A_i\}_{i\in I}$ of countable grupoids can be embedded into a simple groupoid $K(\bigcup_{i\in I} A_i)$ such that $K(\bigcup_{i\in I} A_i)-\bigcup_{i\in I}A_i$ contains only a single element which generates the whole groupoid.

Classification (MSC2000): 20L05

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

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