Original Research
Radical classes, connectednesses and torsion theories
Suid-Afrikaanse Tydskrif vir Natuurwetenskap en Tegnologie | Vol 3, No 1 | a1066 |
DOI: https://doi.org/10.4102/satnt.v3i1.1066
| © 1984 S. Veldsman
| This work is licensed under CC Attribution 4.0
Submitted: 18 March 1984 | Published: 18 March 1984
Submitted: 18 March 1984 | Published: 18 March 1984
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S. Veldsman,, South AfricaFull Text:
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The equality or non-equality of radical classes, torsion classes and connectednesses is investigated in a category that could be any of the concrete categories in which a radical theory, connectednesses theory or a torsion theory have been developed. Among others, it is shown that every connectedness is a radical class. The converse is not true. If, however, a radical class is strict, then it is a connectedness. Furthermore it is proved that every torsion class is a radical class and the converse is not necessarily true. Every radical class with the ADS-property is a torsion class.
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