Semistar operations and standard closure operations

TL;DR

This paper establishes a correspondence between certain finite type closure operations on ideals of a commutative ring and semistar operations of finite type, revealing a structural link in ring theory.

Contribution

It introduces an order isomorphism connecting finite type closure operations and semistar operations, enhancing understanding of their relationship in commutative algebra.

Findings

Demonstrates an order isomorphism between finite type closure operations and semistar operations

Provides a new structural perspective on ideal operations in commutative rings

Bridges concepts of closure and semistar operations in algebraic theory

Abstract

Let $R$ be a commutative ring. It is shown that there is an order isomorphism between a popular class of finite type closure operations on the ideals of $R$ and the poset of semistar operations of finite type.