This book is a self-contained and systematic exposition of the various applications of closure
operations to both commutative and noncommutative algebra. Its primary goal is to apply …

Abstract In 1994, Matsuda and Okabe introduced the notion of semistar operation. This
concept extends the classical concept of star operation (cf. for instance, Gilmer's book …

In the present survey paper, we present several new classes of Hochster's spectral spaces
“occurring in nature,” actually in multiplicative ideal theory, and not linked to or realized in an …

In 1994, Matsuda and Okabe introduced the notion of semistar operation. This concept
extends the classical concept of star operation (cf. for instance, Gilmer's book [4]) and …

Starting from the notion of semistar operation, introduced in 1994 by Okabe and Matsuda
[49], which generalizes the classical concept of star operation (cf. Gilmer's book [27]) and …

We consider properties and applications of a compact, Hausdorff topology called the
“ultrafilter topology” defined on an arbitrary spectral space and we observe that this topology …

This chapter consists of a collection of open problems in commutative algebra. The
collection covers a wide range of topics from both Noetherian and non-Noetherian ring …

Toward the middle of the XlXth century, EE Kummer discovered that the ring of integers of a
cyclotoniic field does not have the unique factorization property and he introduced the …

Let D be an integral domain and★ a semistar operation on D. As a generalization of the
notion of Noetherian domains to the semistar setting, we say that D is a★-Noetherian …

We study almost Dedekind domains with respect to the failure of ideals to have radical
factorization, that is, we study how to measure how far an almost Dedekind domain is from …