… So, in particular, Theorem 22 characterizes when the direct sum of an extending module
and a semisimple module is extending, over a right Noetherian ring. [8, Theorem 4.61, [13, …

… We show that the projective module tensor product of a certain class of contractive left
respectively right modules over properly infinite C* algebras is injective, ie the module tensor …

… and all modules are unitary right modules. Given two R-modules M and N , we say that N is
M-injective if, for … We call N an injective module if N is RR-injective, or equivalently, N is M-…

… any of its direct summands are injective modules (see, eg, … Then we focus on relative
injectivity and ejectivity of modules. … , C3, SIP, etc. in a module, that is, we study conditions of the …

… of working-class simple modules and show that … simple right module is working-class and
call such rings right SW. We show that if a ring R has a projective working-class simple module, …

… Definition We call a class Z of R-modules an injectivity class if it is closed under direct … that
each R-module in Z is injective whence RR in injective. Since quasi-injective modules are in 2, …

… right R-module over a left perfect ring R is maximally injective if and only if it is injective. We
also … that any right R-module over a left perfect ring R is maximally injective if and only if it is …

… injective rings and quasi-injective modules are extended to these modulej. As one application,
we show that, for a finite-dimensional quasi-injective module … : and all modules are unital. …

… of an (M, P)-injective module. This concept contains many versions of … module is said to
be co-cyclic if it is isomorphic to a submodule of the injective envelope of some simple module. …

… injective right A-module is weakly projective. We also study those rings over which every
weakly projective right module is weakly injective… that no other simple module appears in soc(eR…