An error in Corollary 9.32 of [C. Faith, Rings and Things and a Fine Array of Twentieth
Century Associative Algebra, Mathematical Surveys and Monographs, Vol. 65 (American …

We return to the work of Banaschewski and extract from it a theorem of Fuchs, Heinzer, and
Olberding. As an application of Fuchs-Heinzer-Olberding's theorem, we generalize a result …

A commutative ring with unity R is called an EM-ring if for any finitely generated ideal I there
exist a in R and a finitely generated ideal J with Ann (J)= 0 and I= aJ. In this article it is …

For $ k\in\N\cup\{\infty\} $ and $ U $ open in $\R $, let $\C^{\, k}(U) $ be the ring of real
valued functions on $ U $ with the first $ k $ derivatives continuous. It is shown for $ f\in\C …

The article is focuses on the study of the theory of rings of continuous functions with
countable images on a topological space $ X $; the algebraic properties of $ C_c (X) $. The …

For k∈ ℕ∪{∞} and U open in ℝ, let C k (U) be the ring of real valued functions on U with the
first k derivatives continuous. It is shown that for f∈ C k (U) there is g∈ C∞(ℝ) with U⊆ coz …

An element a of a ring R is called a pp (pf) element if the principal ideal< a> is projective
(flat) and a ring is called a pp (pf) ring if its every element is a pp (pf) element. As a natural …

In this paper, we describe some different variations of prime ideals in the context of rings of
continuous functions such as strongly prime ideals, almost prime ideals, n-absorbing ideals …