Our aim is to introduce a ring of some discontinuous real-valued functions defined on a
topological space X. By C (X) F we denote the set of all real-valued functions on the …

In this article we introduce the concept of $ r $-ideals in commutative rings (note: an ideal $ I
$ of a ring $ R $ is called $ r $-ideal, if $ ab\in I $ and ${\rm Ann}(a)=(0) $ imply that $ b\in I …

By a characterization of semiprime SA-rings by Birkenmeier, Ghirati and Taherifar in [4,
Theorem 4.4], and by the topological characterization of C (X) as a Baer-ring by Stone and …

In this paper we study the properties of rAnn (id (R))(the set of right annihilator ideals of R)
as a lattice. We prove that (rAnn (id (R)),⊆) is a Boolean algebra if and only if R is a …

Let $\mathcal {P} $ be an ideal of closed subsets of a topological space $ X $. Consider the
ring, $ C (X) _\mathcal {P} $ of real valued functions on $ X $ whose closure of discontinuity …

A ring R is called a left Ikeda-Nakayama ring (left IN-ring) if the right annihilator of the
intersection of any two left ideals is the sum of the two right annihilators. Also a ring R is …

In this paper, we investigate the conditions for the Mal'cev-Neumann series ring {\Lambda}=
R ((G;{\sigma};{\tau})) to be left fusible and an SA-ring. Also, we show that: if G is a …

Consider the ring $ C_c (X) _F $ of real valued functions which are discontinuous on a finite
set with countable range. We discuss $(\mathcal {Z} _c) _F $-filters on $ X $ and $(\mathcal …

A ring $ R $ is called a left Ikeda-Nakayama ring (left IN-ring) if the right annihilator of the
intersection of any two left ideals is the sum of the two right annihilators. As a generalization …

The purpose of this paper is to study the behavior of the IN and SA property with respect to
the skew power series and Laurent series extensions. For an α-compatible ring R it is shown …