Semisimplicity and von Neumann's regularity

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 1971 Germany English Publisher:Springer Science and Business Media LLCJournal:Semigroup Forum, volume 2, pages 354-361 (issn: 0037-1912, eissn: 1432-2137,

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Authors: Klasa, J.;

doi: 10.1007/bf02572302

Semisimplicity and von Neumann's regularity

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Abstract

The purpose of this paper is to link semigroup theory and category theory by using Green's relations to study regular morphisms and semisimple objects in a category which is filtering in the sense that every morphism admits an epic-monic factorization. For example, the following results are shown for a filtering category C ∶ (1)C is regular if and only if every monic inC is left invertible and every epic inC is right invertible: (2) the monoid of endomorphisms of any semisimple object ofC is regular.

Country

Germany

Related Organizations

Northwestern University
United States
Northern Illinois University
United States
DigiZeitschriften
Germany

Keywords

510.mathematics, Epimorphisms, monomorphisms, special classes of morphisms, null morphisms, Article

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