a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable ...

We establish equivalent conditions under which every right Rmodule has an epic X -envelope, when X is a Tor-orthogonal class of left-Rmodules. As particular cases, one may recover and complete known results on various generalizations of flatness. MSC 2000. 16D50, 16D40.

For a unitary right module M , there are two known partitions of simple modules in the category σ[M ]: the first one divides them into M -injective modules and M -small modules, while the second one divides them into M -projective modules and M -singular modules. We study inclusions between the first two and the last two classes of simple modules in terms of some associated radicals and proper ...

An R-module is called semi-endosimple if it has no proper fully invariant essential submodules. For a quasi-projective retractable module MR we show that M is finitely generated semi-endosimple if and only if the endomorphism ring of M is a finite direct sum of simple rings. For an arbitrary module M , conditions equivalent to the semi-endosimplicity of its quasi-injective hull are found. As co...

PURPOSE Both cannulated cancellous screw (CCS) and sliding hip screw (SHS) are used in femoral neck fracture fixations, but which is superior is yet to be determined. This study was aimed to compare the clinicoradiological outcome of femoral neck fracture treated with SHS or CCS in young adults. METHODS Adults (16e60 years) with femoral neck fracture were divided into Group 1 fixed with SHS a...

The purpose of this paper is to show that a duality exists between the fractional ideal approach [23, 26] and the operator-theoretic approach [4, 6, 8, 9, 33, 34] to stabilization problems. In particular, this duality helps us to understand how the algebraic properties of systems are reflected by the operator-theoretic approach and conversely. In terms of modules, we characterize the domain and...

let r be a commutative ring with non-zero identity and m be a unital r-module. then the concept of quasi-secondary submodules of m is introduced and some results concerning this class of submodules is obtained