زیرحلقه‌های ماکسیمال در دامنه‌های پروفر

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی ،دانشکده علوم ریاضی و کامپیوتر،دانشگاه شهید چمران اهواز ،اهواز،ایران

چکیده

یک زیرحلقه ی سره یکانی از یک حلقه ی R را ماکسیمال می نامیم، هرگاه در بین زیرحلقه های سره ی R با رابطه شمول ماکسیمال باشد. دراین مقاله می‌خواهیم شرایطی را بررسی می کنیم که یک دامنه ی پروفر تحت آن، دارای زیرحلقه‌ی ماکسیمال باشد. هم چنین می‌خواهیم به بررسی انتقال ویژگی پروفر، بزوت و ... از یک دامنه به زیرحلقه‌ی ماکسیمال آن و برعکس بپردازیم.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Maximal Subrings of Prufer Domains

نویسندگان [English]

  • Alborz Azarang
  • Mohammadreza Alinaghizadeh
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz-Iran
چکیده [English]

A proper unital subring of a ring R is called a maximal subring, if it is maximal with inclusion between proper subrings of R. In this paper we present conditions under which a Pr"{u}fer domain has a maximal subring. We study the Pr"{u}fer and B'{e}zout properties which are shared between an integral domain and its maximal subrings too.

کلیدواژه‌ها [English]

  • Prufer domain
  • Bezout domain
  • Maximal Subring
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