Convex Ideals of Partially Pseudo-Ordered Rings

被引：0
作者：
E. E. Shirshova [1 ]
机构：
[1] Moscow Pedagogical State University, Moscow
来源：
Journal of Mathematical Sciences | 2024年 / 283卷 / 6期
关键词：
D O I：
10.1007/s10958-024-07323-6
中图分类号：
学科分类号：
摘要：
Characteristics of partially pseudo-ordered (K-ordered) rings are considered. Properties of the set of all convex directed ideals in pseudo-ordered rings are described. It is shown that convex directed ideals play for the theory of partially pseudo-ordered rings the same role as convex directed subgroups for the theory of partially ordered groups. Necessary and sufficient conditions for a convex directed ideal of an AO-pseudo-ordered ring to be a rectifying ideal are obtained. We show that the set of all rectifying directed ideals of an AO-pseudo-ordered ring form the root system for the lattice of all convex directed ideals of that ring. Properties of regular ideals for partially pseudo-ordered rings are investigated. Some results are proved concerning convex directed ideals of pseudo-lattice pseudo-ordered rings. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.
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页码：948 / 961
页数：13
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