The aim of this paper is twofold. Firstly, to give short proofs of the celebrated results of Rudd
(1970), De Marco (1972), Brookshear (1977), Neville (1990), and Vechtomov (1996) with the …

In this paper we show that the set of z-ideals and the set of z∘ ideals (= d-ideals) of the
classical ring of quotients q (R)(q (X)) of a reduced ring R with property A (C (X)) coincide …

fies the descending chain condition modulo its radical. In his paper, Kothe shows among
other things that each minimal non-nil right ideal of an arbitrary ring contains an idempotent …

It is well known that a commutative ring R is complemented (that is, given a∈ R there exists
b∈ R such that ab= 0 and a+ b is a regular element) if and only if the total ring of quotients of …

Let 𝐴 (𝑋) be a subring of 𝐶 (𝑋) that contains 𝐶*(𝑋). In Redlin and Watson (1987) and in
Panman et al.(2012), correspondences 𝒵𝐴 and ℨ𝐴 are defined between ideals in 𝐴 (𝑋) and …

In this note we prove that the centre C of a right hereditary ring R is hereditary ifR is a finitely
generated C-module. It is shown by an example due to LW Small that a right hereditary ring …

Let us recall from [C, Definition l] that a module is said to be DICC if any chain of
submodules indexed by the integers H stabilizes either to the right or to the left (or to both …

One Counterexample for Two Open Questions about the Rings R(X) and R<X> Page 1 Ž .
Journal of Algebra 222, 424427 1999 doi:10.1006rjabr.1999.8009, available online at http:rrwww.idealibrary.com …

We introduce the notion of a relatively adequate element of a commutative ring, which is not
necessary a domain, investigate properties of such elements, and on the basis of this …

We say that a commutative ring $ R $ is a $ u $-ring provided $ R $ has the property that an
ideal contained in a finite union of ideals must be contained in one of those ideals; and a …