Several parallel characterizations of the FIP and FCP properties are given. Also, a number of
results about FCP are generalized from domains to arbitrary (commutative) rings. Let R⊆ S …

We establish several characterizations of maximal non-Prüfer and maximal non-integrally
closed subrings of a field. Special attention is given when finiteness conditions are satisfied …

Let R⊂ S be an extension of integral domains, and let be the integral closure of R in S. This
work's research is devoted to a deeper study of [R, S], the set of intermediate rings between …

Let X be a nonempty set and P (X) the power set of X. The aim of this paper is to identify the
unital subrings of P (X) and to compute its cardinality when it is finite. It is proved that any …

Numerical characterizations of some integral domains Page 1 Monatsh Math (2011) 164:171–181
DOI 10.1007/s00605-010-0205-0 Numerical characterizations of some integral domains Ali …

We establish several new characterizations of maximal non-valuation subrings of a field
involving several concepts of commutative algebra related to the set of prime ideals and the …

It is shown that RgMax (R) is infinite for certain commutative rings, where RgMax (R)
denotes the set of all maximal subrings of a ring R. It is observed that whenever R is a ring …

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 …

Let R, T be commutative rings with identity such that R⊆ T. We recall that R⊆ T is called a λ-
extension of rings if the set of all subrings of T containing R (the “intermediate rings”) is …

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 …