Let R be a nonzero associative ring with identity. It is proved that R is a finite Boolean ring if
(and only if) 1 is the only unit of R and there exists a finite maximal chain C each of whose n …

We investigate integral domains with only finitely many overrings and establish several new
sharp inequalities relating the cardinality of the set of all overrings, the Krull dimension, and …

Subrings of a power set and clopen topologies Page 1 Journal of Algebra and Its Applications
Vol. 20, No. 12 (2021) 2150224 (13 pages) c© World Scientific Publishing Company DOI …

Let X be a set and f: X→ X be a map. We denote by 𝒫 (f) the topology defined on X whose
closed sets are the subsets A of X with f (A)⊆ A. A topology on X is said to be a primal …

We establish several finiteness characterizations and equations for the cardinality and the
length of the set of overrings of rings with nontrivial zero divisors and integrally closed in …

Let $ X $ be a Tychonoff space. Let $\mathfrak {A}:= C (X) $ and $\mathfrak {A}^*:= C^*(X) $
denote, respectively, the ring of all real-valued continuous functions and the ring of all …

A NOTE ON CLOPEN TOPOLOGIES Page 1 Palestine Journal of Mathematics Vol. 11(4)(2022)
, 26–27 © Palestine Polytechnic University-PPU 2022 A NOTE ON CLOPEN TOPOLOGIES …