Minimal formations of universal algebras
Wenbin Guo ; K.P. Shum
Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001), p. 201-205 / Harvested from The Polish Digital Mathematics Library
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A class ℱ of universal algebras is called a formation if the following conditions are satisfied: 1) Any homomorphic image of A ∈ ℱ is in ℱ; 2) If α₁, α₂ are congruences on A and A/αi∈ℱ, i = 1,2, then A/(α₁∩α₂) ∈ ℱ. We prove that any formation generated by a simple algebra with permutable congruences is minimal, and hence any formation containing a simple algebra, with permutable congruences, contains a minimum subformation. This result gives a partial answer to an open problem of Shemetkov and Skiba on formations of finite universal algebras proposed in 1989.

Publié le : 2001-01-01
EUDML-ID : urn:eudml:doc:287759 
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Wenbin Guo; K.P. Shum. Minimal formations of universal algebras. Discussiones Mathematicae - General Algebra and Applications, Tome 21 (2001) pp. 201-205. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1037/

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