Varieties without minimal generators |
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Authors: | Hans-E Porst Jiří Rosický |
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Institution: | (1) University of Bremen, P.O. Box 330440, D-28334 Bremen, Germany, e-mail: porst@math.uni-bremen.de, DE;(2) Masaryk University, Janáčkovo nám 2a, 66295 Brno, Czech Republic, e-mail: rosicky@math.muni.cz, CZ |
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Abstract: | While many familiar varieties have a minimal varietal generator, i.e., a regular projective finitely presentable regular
generator such that none of its retracts is a regular generator, and even a unique one, we present (a) a variety having no
minimal varietal generator at all and (b) a variety having two non-isomorphic minimal varietal generators. Moreover we demonstrate
that the same effects can happen with respect to a weaker notion of minimality and are common even in module categories.
Received April 7, 1999; accepted in final form July 10, 2000. |
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Keywords: | : Varieties regular projective regular generator equational representation of varieties |
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