Generalizations of Regular Sequences and Grade, and Problems Related to Applications

概要

近年の可換環論において，Noether とは限らない環上の加群についてのホモロジー代数的な考察の重要度は年々高まっている．本講演では，正則列，grade といった概念の一般化とその応用について紹介し，講演者が得た結果に触れる．本稿の内容は [And22] と，未発表の内容に基づく．

In recent years, within commutative algebra, the importance of homological algebraic studies concerning modules over rings that are not necessarily Noetherian has been growing year by year. In this talk, we will introduce generalizations of concepts such as regular sequences and grade, along with their applications, and touch upon results obtained by the speaker. The content of this manuscript is based on [And22] and unpublished work.