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On the radical classes and the transfree-images of rings

On the radical classes and the transfree-images of rings Acta Mathematica Academiae Scientiarum Hungaricae Tomus 35 (3--4), (1980), 399--402. ON THE RADICAL CLASSES AND THE TRANSFREE- IMAGES OF RINGS By TRAN TRONG HUE and F. SZ/~SZ (Budapest) 1. The purpose of this note is to consider the relation between the transfree- images and the radical classes in category of associative rings. This stays in connec- tion to the solution of problem 8 of [2]. The notion of transfree-images is dual to that of subdirect embedding (cf. [3]). An object .4 of the category cd is said to be a transfree-image of the free product If .4i(~i) if there exists an epimorphism V://.4i(~Oi) "~`4 such that all maps 7: 0i: iEl iEI A~`4, iEI are normal monomorphisms. Instead of a transfree-image of the free product /_]" Ai(Qi) we speak of a trans- iEI free-image of the objects .4i, iEL A class M of rings is said to be a radical class in sense of Amitsur and Kurosh if the following conditions are satisfied: (i) M is homomorphically closed. (ii) The sum of all M-ideals of a ring .4 is an M-ideal. (iii) M is closed under extensions, that is if B and .4/BEM then also .4EM. The lower radical http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematica Academiae Scientiarum Hungarica Springer Journals

On the radical classes and the transfree-images of rings

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Publisher
Springer Journals
Copyright
Copyright
Subject
Mathematics; Mathematics, general
ISSN
0001-5954
eISSN
1588-2632
DOI
10.1007/BF01886310
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Abstract

Acta Mathematica Academiae Scientiarum Hungaricae Tomus 35 (3--4), (1980), 399--402. ON THE RADICAL CLASSES AND THE TRANSFREE- IMAGES OF RINGS By TRAN TRONG HUE and F. SZ/~SZ (Budapest) 1. The purpose of this note is to consider the relation between the transfree- images and the radical classes in category of associative rings. This stays in connec- tion to the solution of problem 8 of [2]. The notion of transfree-images is dual to that of subdirect embedding (cf. [3]). An object .4 of the category cd is said to be a transfree-image of the free product If .4i(~i) if there exists an epimorphism V://.4i(~Oi) "~`4 such that all maps 7: 0i: iEl iEI A~`4, iEI are normal monomorphisms. Instead of a transfree-image of the free product /_]" Ai(Qi) we speak of a trans- iEI free-image of the objects .4i, iEL A class M of rings is said to be a radical class in sense of Amitsur and Kurosh if the following conditions are satisfied: (i) M is homomorphically closed. (ii) The sum of all M-ideals of a ring .4 is an M-ideal. (iii) M is closed under extensions, that is if B and .4/BEM then also .4EM. The lower radical

Journal

Acta Mathematica Academiae Scientiarum Hungarica – Springer Journals

Published: Jun 15, 2005

References

  • Radikale der Ringe
    Szász, F.
  • On the dualization of subdirect embeddings
    Szász, F.; Wiegandt, R.