In this expository paper, we survey results on the concept of a hull of a ring or a module with
respect to a specific class of rings or modules. A hull is a ring or a module which is minimal …

Throughout R will denote an associative ring with identity. Let Zℓ (R) be the left singular
ideal of R. It is well known that Zℓ (R)= 0 if and only if the left maximal ring of quotients of R …

Let e and f be primitive idempotents in a semiperfect ring R with radical J. Suppose that (i) fR
fJ≅ Soc (eR R), which is essential in eRR; and (ii) Re Je≅ Soc (RRf), which is essential in …

In F. Azarpanah et al.(2008)[3] the authors have given some algebraic properties of the ring
C (X)/CF (X), where CF (X)= O β X∖ I (X). In this paper, first, we show that C (X)/CF (X) is a C …

This paper is concerned with unital ring extensions of a simple unit-regular ring I by a simple
unit-regular ring S with identity, that is, with unit-regular rings R with identity containing an …

In this article we observe that C(X) is integral over I+\mathbbR if and only if I is of the form of
a finite intersection of real maximal ideals. The integral closure of a subring I+\mathbbR is …

In this article we investigate the transfer of the notions of elementary divisor ring, Hermite
ring, Bezout ring, and arithmetical ring to trivial ring extensions of commutative rings by …

For a ring R, we investigate and determine “minimal” right essential overrings (right ring
hulls) belonging to certain classes which are generated by R and subsets of the central …

Rings having von Neumann regular classical left quotient rings 0 arc considered¡ it the first
section ol'this note. Conditions for Qto be strongly regular and semi-simple Artinian arc …

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 …