On the existence and non-existence of complementary radical and semisimple classes

S. Veldsman, R. Wiegandt

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In certain categories of mathematical structures, non-trivial complementary radical classes (torsion classes or connectednesses) can be found. The question is why this is true for some but not for all categories. The answer depends on the embedding of trivial objects into nontrivial objects and is given by our main result: Any ‘reasonable’ category has no non-trivial complementary radical and semisimple classes if and only if for every trivial object T and every non-trivial object A there is a morphism T → A. Roughly, a ‘reasonable’ category in our sense is one with at least one object into which a terminal object can be embedded and has finite products, coproducts or lexicographic products.

Original languageEnglish
Pages (from-to)213-224
Number of pages12
JournalQuaestiones Mathematicae
Volume7
Issue number3
DOIs
Publication statusPublished - 1984

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Semisimple
Nonexistence
Trivial
Lexicographic Product
Coproducts
Morphism
Torsion
Class
Object
If and only if

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

On the existence and non-existence of complementary radical and semisimple classes. / Veldsman, S.; Wiegandt, R.

In: Quaestiones Mathematicae, Vol. 7, No. 3, 1984, p. 213-224.

Research output: Contribution to journalArticle

Veldsman, S. ; Wiegandt, R. / On the existence and non-existence of complementary radical and semisimple classes. In: Quaestiones Mathematicae. 1984 ; Vol. 7, No. 3. pp. 213-224.
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