extensions, minimality and idempotents of certain semigroup compactifications

thesis
abstract

در فصل اول مقدمات و پیش نیازهای لازم برای فصل های بعدی فراهم گردیده است . در فصل دوم مساله توسیع مورد توجه قرار گرفته و ابتدا شرایطی که تحت آن از یک فشرده سازی نیم گروهی خاص یک زیرگروه نرمال بسته یک گروه به یک فشرده سازی متناظر با فشرده سازی اولیه برای گروه رسید مورد بررسی قرار گرفته و سپس ارتیاط بین ساختارهای مختلف روی این دو فشرده سازی از جمله ایده آل های مینیمال چپ و راست و... مورد بررسی قرار گرفته است . در این راستا مفهوم فشرده سازی تحت مزدوج پایا تعریف و مورد بررسی قرار گرفته است . در فصل سوم ابتدا با کارهای chou در زمینه گروههای تقریبا دوره ای مینیمال آشنا شده و سپس به کمک مقالات junghenn به توسیع این مفهوم روی نیم گروهها پرداخته ایم و نهایتا در فصل چهارم با پیگیری کارهای ruppert در زمینه ساخت توابع دوره ای، توابع تقریبا دوره ای خاصی مطرح و به کمک آنها با این سوال ruppert که آیا مجموعه عناصر خودتوان در یک فشرده سازی نیم توپولوژیکی مجموعه اعداد طبیعی بسته است یا نه؟ پاسخ منفی داده شده است .

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document type: thesis

وزارت علوم، تحقیقات و فناوری - دانشگاه فردوسی مشهد - دانشکده علوم

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