Sulle classi filtrali di algebre
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Generalizing results of , we show that if a classK of algebras is filtral (as defined byMagari ), then so is the class of all simple algebras in the varietyW K generated byK, and these simple objects are precisely all subalgebras of all ultraproducts of copies of algebras inK. All algebras inW K are semisimple and regular. We then obtain charac terizations of filtral and semifiltral classes of algebras in terms of the existence of certain types of operations in these algebras, and illustrate our results with examples, mainly from ring theory.
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- R. S. Pierce,Modules over Commutative Regular Rings, Mem. A.M.S., n. 70 (1967).Google Scholar