Abstract Let\(R\) be a ring, let\(M\) be a left\(R\)-module, and let\(U, V, F\) be submodules
of\(M\) with\(F\) proper. We call\(V\) an\(F\)-supplement of\(U\) in\(M\) if\(V\) is minimal in the …

Let R be a commutative ring with a nonzero identity and M an R-module. Set ϕ-tor (M)={x∈
M| sx= 0 for some s∈ R∖ Nil (R)}, if ϕ-tor (M)= M then M is called a ϕ-torsion module. An R …

In this paper, we introduce and study the concept of FI-hollow-lifting modules which is a
proper generalization of hollow-lifting modules. We say M called a fully invariant hollow …

In this paper, we introduce the notion of fpn-injective and fpn-flat modules, and investigate
their properties. In particular, we prove that every left R-module has an fpn-injective cover …

1. Introduction Page 1 TAIWANESE JOURNAL OF MATHEMATICS Vol. 22, No. 3, pp. 545–565,
June 2018 DOI: 10.11650/tjm/171102 Primitive Submodules, Co-semisimple and Regular …

For right R-modules M and N, if every monomorphism from a fully invariant M-cyclic
submodule s (M) of M to N can be extended to a homomorphism from M to N, then N is …

In this paper, we study some more properties on direct-injective modules in the context of
endoregular, SSP and SIP modules. We find the equivalent condition for a directinjective …

In this paper we generalize the notion of pure injectivity of modules by introducing what we
call a pure Baer injective module. Some properties and some characterization of such …