Modules satisfying double chain condition on uncountably generated submodules

داودیان, مریم

doi:10.22055/jamm.2024.45312.2227

Modules satisfying double chain condition on uncountably generated submodules

نوع مقاله : مقاله پژوهشی

نویسنده

مریم داودیان

گروه ریاضی، دانشگاه شهید چمران اهواز، اهواز، ایران

10.22055/jamm.2024.45312.2227

چکیده

In this article, we study modules that satisfy the double infinite chain condition on uncountably generated submodules, briefly called u.c.g.-DICC modules. We show that if a quotient finite dimensional module M satisfies the double infinite chain condition on uncountably generated submodules, then it has Krull dimension. We study submodules N of a module M such that whenever $\frac{M}{N}$ satisfies the double infinite chain condition so does M. Moreover, we observe that an α-atomic module, where α>\ω_{1}$ is an ordinal number, satisfies the previous chain condition if and only if it satisfies the descending chain condition on uncountably generated submodules.

کلیدواژه‌ها

موضوعات

جبر

عنوان مقاله [English]

Modules satisfying double chain condition on uncountably generated submodules

نویسنده [English]

Maryam Davoudian

Department of mathematics, Shahid Chamran university of Ahvaz, Ahvaz, Iran

چکیده [English]

In this article, we study modules that satisfy the double infinite chain condition on uncountably generated submodules, briefly called $u.c.g.-DICC$ modules. We show that if a quotient finite dimensional module $M$ satisfies the double infinite chain condition on uncountably generated submodules, then it has Krull dimension. We study submodules $N$ of a module $M$ such that whenever $\frac{M}{N}$ satisfies the double infinite chain condition so does $M$.
Moreover, we observe that an $\alpha $-atomic module, where $\alpha>\omega_{1}$ is an ordinal number, satisfies the previous chain if and only if it satisfies the descending chain condition on uncountably generated submodules.

کلیدواژه‌ها [English]

uncountably generated modules
Krull dimension
DICC-modules
u.c.g.-DICC modules

مراجع

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