Radical and Torsion Theory for Acts
| Autor: | R. Wiegandt |
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| Rok vydání: | 2006 |
| Předmět: | |
| Zdroj: | Semigroup Forum. 72:312-328 |
| ISSN: | 1432-2137 0037-1912 |
| DOI: | 10.1007/s00233-005-0546-5 |
| Popis: | After recapitulating the rudiments of the Kurosh-Amitsur radical theory of S-acts, hereditary radicals are discussed. The hereditary Hoehnke radical assignments r which designate a Rees congruence r(A) to each S-act A, are the hereditary Kurosh-Amitsur radical assignments. Then the corresponding radical as well as semisimple classes are characterized. Equivalence classes of injective S-acts determine hereditary torsion assignments t, these are just the hereditary Hoehnke radicals, but the congruence t(A) of A need not be a Rees congruence. Torsion and torsionfree classes are characterized; several hereditary torsion assignments may determine the same torsion class which is always a radical class closed under taking subacts. Examples show that a hereditary torsion assignment need not be a hereditary radical. |
| Databáze: | OpenAIRE |
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