Residual quotient fuzzy subset in near-rings.
Right Symbolic Powers and Classical Localization in Right Noetherian Rings.
Right Utumi p.p.-rings
Ringe mit nichtkommutativer Addition I.
Ringe mit verallgemeinerter Kupischreihe.
Ringe mit verallgemeinerter Kupischreihe. II.
Ringepimorphismen und Morita-projektive Moduln über kommutativen Dedekind-Ringen.
Rings admitting torsion injective covers
Rings decomposed into direct sums of J-rings and nil rings.
Rings Graded By a Generalized Group
The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups. We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. We prove that if I is a complete homogeneous ideal of a G-graded ring R, then R/I is a G-graded ring.We deduce a characterization of the maximal ideals of a G-graded ring which are homogeneous. We also prove that if R is a Noetherian graded ring, then each summand of it is also a Noetherian module..
Rings in which every proper right ideal is maximal
Rings in which ideals are annihilators
Rings which are semilattices of archimedean semigroups.
Rings which have projective coflat module
Rings whose class of projective modules is socle fine.
Rings whose modules are finitely generated over their endomorphism rings
A module M is called finendo (cofinendo) if M is finitely generated (respectively, finitely cogenerated) over its endomorphism ring. It is proved that if R is any hereditary ring, then the following conditions are equivalent: (a) Every right R-module is finendo; (b) Every left R-module is cofinendo; (c) R is left pure semisimple and every finitely generated indecomposable left R-module is cofinendo; (d) R is left pure semisimple and every finitely generated indecomposable left R-module is finendo;...
Rings whose modules have maximal submodules.
A ring R is a right max ring if every right module M ≠ 0 has at least one maximal submodule. It suffices to check for maximal submodules of a single module and its submodules in order to test for a max ring; namely, any cogenerating module E of mod-R; also it suffices to check the submodules of the injective hull E(V) of each simple module V (Theorem 1). Another test is transfinite nilpotence of the radical of E in the sense that radα E = 0; equivalently, there is an ordinal α such that radα(E(V))...
Rings whose nonsingular right modules are -projective
A right -module is called -projective provided that it is projective relative to the right -module . This paper deals with the rings whose all nonsingular right modules are -projective. For a right nonsingular ring , we prove that is of finite Goldie rank and all nonsingular right -modules are -projective if and only if is right finitely - and flat right -modules are -projective. Then, -projectivity of the class of nonsingular injective right modules is also considered. Over right...
Rings with a certain condition on subsemigroups.
Rings with a finite set of nonnilpotents.