Generalized projectivity. II.
Josef Jirásko · Czech digital mathematics library · 1979
Recently in [111 the (r,i,s,j)-projectivity (i.e. the projectivity with respect to two preradicals r and s) has been investigated.In many cases the (r,i,s,j)-projectivity is reduced to the (l,t)-projectivity for some preradical t.It is shown that a module P is (l.r)-projective if and only if P/ch(r)(P) is projective in R/r(ft)-mod# In § 2 we shall show that the concepts of (l,r)-projectivity and the strongly M-projectivity which is studied by K. Varadarajan in £181 are the same.Further, in the study (r,2)-projectivity, where r is an idempotent preradical and # is pseudohereditary, r can be replaced by a hereditary radical.§ 3 is devoted to the study of (r ?i,s,j)-quasiprojective modules.Some of these results are motivated by J.S. Golan's paper 183 on quasiprojective modules.