Transfinite normal and composition series of modules
Ruslan Sharipov
TL;DR
This paper explores the structure of modules through transfinite normal and composition series indexed by ordinal numbers, discussing their properties and the applicability of the Jordan-Hölder theorem in this context.
Contribution
It introduces the concept of transfinite series of modules and extends classical theorems to this broader ordinal framework.
Findings
Establishment of properties of transfinite series
Extension of Jordan-Hölder theorem to transfinite series
Insights into module decomposition using ordinal-indexed series
Abstract
Normal and composition series of modules enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is discussed.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Rings, Modules, and Algebras