2019/07/09 by Muhammad Zafrullah, Zafrullah, Muhammad
Mathematics · #06F20 (Secondary) #13A15 (Primary) #13G05 #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AC #msc:06F20 #msc:13A15 #msc:13G05
paper · pdf · doi:10.48550/arxiv.1907.04384
openalex publication_date 2019/07/09 · arxiv created 2021/12/30 · arxiv updated 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let ∗ be a star operation of finite character. Call a ∗ -ideal I of finite type a ∗ -homogeneous ideal if I is contained in a unique maximal ∗ -ideal M=M(I). A maximal ∗ -ideal that contains a ∗ -homogeneous ideal is called ∗ -potent and the same name bears a domain all of whose maximal ∗ -ideals are ∗ -potent. One among the various aims of this article is to indicate what makes a ∗ -ideal of finite type a ∗ -homogeneous ideal, where and how we can find one, what they can do and how this notion came to be. We also prove some results of current interest in ring theory using some ideas from this author's joint work in \citeLYZ 2014 on partially ordered monoids. For example we characterize when a commutative Riesz monoid generates a Riesz group.