Open AccessRadical classes, connectednesses and torsion theories
Author(s) -
Stefan Veldsman
Publication year - 1984
Publication title -
suid-afrikaanse tydskrif vir natuurwetenskap en tegnologie/die suid-afrikaanse tydskrif vir natuurwetenskap en tegnologie
Language(s) - English
Resource type - Journals
eISSN - 2222-4173
pISSN - 0254-3486
DOI - 10.4102/satnt.v3i1.1066
Subject(s) - converse , torsion (gastropod) , social connectedness , class (philosophy) , mathematics , pure mathematics , epistemology , social psychology , philosophy , psychology , geometry , biology , zoology
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