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 …

A ring extension R⊆ S is said to be FO if it has only finitely many intermediate rings. R⊆ S is
said to be FC if each chain of distinct intermediate rings in this extension is finite. We …

Let R⊂ S and S⊂ T be minimal ring extensions of (commutative) rings. Shapiro and the
author recently gave 13 mutually exclusive conditions on these minimal ring extensions and …

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 …

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 …

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 …

Let R⊆ S be an extension of integral domains with only finitely many intermediate rings,
where R is not a field and S is not necessarily the quotient field of R or R is not necessarily …