A Krull module that is not strongly Krull

Communications in Algebra 2026

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Authors: Mu’amar Musa Nurwigantara, Indah Emilia Wijayanti, Hidetoshi Marubayashi, Sri Wahyuni
DOI: 10.1080/00927872.2025.2588374
Cited by: 0
References: 6

Abstract

We defined Krull modules over an integral domain as a completely integrally closed module satisfying ascending chain condition on integral v-submodules. However, if the dimension of the module of fractions over the quotient field is more than 1, then there are many non-integral submodules. Thus, we then defined strongly Krull modules which involves all non-zero submodules (whether it’s integral or non-integral). In this paper, we will prove that the Cartesian product of the ring of integers and the ring of p-integers is an example of Krull module which is not strongly Krull, showing that our definition of strongly Krull modules is indeed properly stronger than Krull modules.

Fields of Study & Subjects

Rings Modules and Algebras Commutative Algebra and Its Applications Algebraic structures and combinatorial models

Publication details

Journal / source
Communications in Algebra
Volume
54
Issue
7
Pages
2847–2853
Publication date
28 January 2026
Language
EN