PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 38(52), pp. 5163 (1985) 

QUASIRADICALS AND RADICALS IN CATEGORIESA. Buys and S. VeldsmanDepartment of Mathematics, University of Port Elizabeth, 6000 Porth Elizabeth, Republic of South AfricaAbstract: In a category $\Cal K$, if $\Cal E$ is a class of epimorphisms and $\Cal M$ a class of monomorphisms, a funtion $J_r$ called an $(\Cal E, \overline{\Cal M})$quasiradical, is defined which assigns to an object an $\Cal M$sink and a function $J_c$, called an $(\overline{\Cal E},\Cal M)$quasicoradical, is defined which assigns to an object an $\Cal E$source. With $J_r$ are associated two object classes {\bf R}$_r$ and {\bf S}$_r$ called the quasiradical class and the quasisemisimple class respectively. With $J_c$ are associated two object classes {\bf R}$_c$ and {\bf S}$_c$, called the quasicoradical class and the quasicosemisimple class respectively. Using these notions, an $(\Cal E,\overline{\Cal M})$radical is a pair $(J_r,J_c)$ where $J_r$, is a quasiradical, $J_c$ a quasicoradical and for which ${\bold R}_r={\bold R}_c$ and ${\bold S}_r={\bold S}_c$. Among others it is shown that ${\bold R}_r={\bold R}_c$ is a radical class and ${\bold S}_r= {\bold S}_c$ is a semisimple class. Classification (MSC2000): 18E40 Full text of the article:
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