Radical and Torsion Theory for Acts |
| |
Authors: | Richard Wiegandt |
| |
Institution: | (1) A. Renyi Institute of Mathematics, P. O. Box 127, H–1364 Budapest, Hungary |
| |
Abstract: | 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|