All rings are assumed to be associative and (except for nil-rings and some stipulated cases)
to have nonzero identity elements. Expressions such as a “Noetherian ring” mean that the …

Rings over which every nonzero right module has a maximal submodule are called right
Bass rings. For a ring A module-finite over its center C, the equivalence of the following …

Right Bass rings are investigated, that is, rings over which any nonzero right module has a
maximal submodule. In particular, it is proved that if any prime quotient ring of a ring A is …

A ring R is said to have the ascending chain condition on cyclic left modules if each
ascending chain of cyclic submodules of a module terminates. If a ring R has this property …

Proof. For any ring R with identity, it is easy to see that a right ideal/of R is generated by an
idempotent if and only if/is a direct summand of the right iϋ-module RR. If I is an injective …

Let R be an associative ring with identity. Then the left socle of R is a direct summand of R
as a right R-module if and only if it is projective as a left R-module and contains no infinite …

This paper deals with the relationship between a ring T and the idealizer R of a right ideal M
of T.[The ring R is the largest subring of T which contains M as a two-sided ideal.] Assuming …

In this paper we study two types of finite associative rings, namely, rings with only one
maximal subring and those with exactly two maximal subrings. It is easy to see that the …

Rings over which every module has a maximal submodule Page 1 RINGS OVER WHICtt
EVERY MODULE HAS A MAXIMAL SUBMODULE LA Koifman UDC 512.4 We consider Bass's …

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 …