A ring $ R $, possibly with no identity, is called an ${I_0} $-ring if each one-sided ideal not
contained in the Jacobson radical $ J (R) $ contains a nonzero idempotent. If, in addition …

The following conditions are shown to be equivalent: 1) ring A is generalized uniserial (not
necessarily artinian); 2) every finitely presented A module is semiserial; 3) A is semiperfect …

Let R be a ring with Jacobson radical J. Bass [1] called R semi-perfect if the factor ring R/J is
semi-simple Artinian and every idempotent of R/J can be lifted to an idempotent of R. He …

The complete (or maximal) ring of right quotients of an associative ring R was introduced by
Utumi in [20]. This concept has been studied by many authors, but in most cases the …

A module is called uniserial (or often simply serial) in case its lattice of submodules is a
chain. An artinian ring is called serial (or generalized uniserial) in case each of its …

For a ring $ R $ which satisfies a polynomial identity we show that the following are
equivalent:(1) $ R $ is von Neumann regular,(2) each two-sided ideal of $ R $ is idempotent …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …

2. Background. As mentioned in the introduction, Harada has studied the conditions:(*)
Every non-small right R-module contains a non-zero injective submodule.(*)* Every non …

We prove in this paper that fifteen classes of rings coincide with the class of rings named in
the title. One of them is the class of rings R such that X2= X for each R-ideal X: we shall refer …

A semigroup (R,⋅) is said to be a unique addition ring (UA-ring) if there exists a unique
binary operation+ making (R,⋅,+) into a ring. All our results can be presented in this …