On $\ast$-homogeneous ideals

Abstract

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 [37] on partially ordered monoids. We characterize when a commutative Riesz monoid generates a Riesz group.