Semigroups for which every right congruence of finite index is finitely generated

Modules for which every non-cosingular submodule is a summand

‎A module $M$ is lifting if and only if $M$ is amply supplemented and‎ ‎every coclosed submodule of $M$ is a direct summand‎. ‎In this paper‎, ‎we are‎ ‎interested in a generalization of lifting modules by removing the condition‎"‎amply supplemented‎" ‎and just focus on modules such that every non-cosingular‎ ‎submodule of them is a summand‎. ‎We call these modules NS‎. ‎We investigate some gen...

Rings of Continuous Functions in Which Every Finitely Generated Ideal is Principal

Rings for which every simple module is almost injective

We introduce the class of “right almost V-rings” which is properly between the classes of right V-rings and right good rings. A ring R is called a right almost V-ring if every simple R-module is almost injective. It is proved that R is a right almost V-ring if and only if for every R-module M, any complement of every simple submodule of M is a direct summand. Moreover, R is a right almost V-rin...

Commutative rings in which every finitely generated ideal is quasi-projective

This paper studies the multiplicative ideal structure of commutative rings in which every finitely generated ideal is quasi-projective. Section 2 provides some preliminaries on quasi-projective modules over commutative rings. Section 3 investigates the correlation with well-known Prüfer conditions; namely, we prove that this class of rings stands strictly between the two classes of arithmetical...

Groups in which every subgroup has finite index in its Frattini closure

‎In 1970‎, ‎Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali‎, ‎ Atti Accad‎. ‎Naz‎. ‎Lincei Rend‎. ‎Cl‎. ‎Sci‎. ‎Fis‎. ‎Mat‎. ‎Natur. 48 (1970)‎, ‎559--562.] gave a complete description of the structure of soluble $IM$-groups‎, ‎i.e.‎, ‎groups in which every subgroup can be obtained as intersection of maximal subgroups‎. ‎A group $G$ is said to have the $FM$...