Rings of differential operators over rational affine curves
Rings of Quotients of Perfect Rings.
Rings of skew polynomials in algebraical approach to control theory
Rings radical over P.I. subrings
Rings -radical over -subrings
Rings satisfying a certain idempotency condition
Rings satisfying certain chain conditions.
Rings which are semilattices of archimedean semigroups.
Rings which have projective coflat module
Rings whose class of projective modules is socle fine.
Rings whose Elements are Quasi-Regular or Regular
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 whose proper factors are right perfect
We show that practically all the properties of almost perfect rings, proved by Bazzoni and Salce [Colloq. Math. 95 (2003)] for commutative rings, also hold in the non-commutative setting.
Rings with a certain condition on subsemigroups.
Rings with a finite set of nonnilpotents.
Rings with Dense Quasi-Centre.
Rings with indecomposable modules local.
Rings with involution whose symmetric elements are central.