Mathematical Researches
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فشردهسازی برای قابهای کاملاً منظم بر اساس قسمت متممصفرشان
Ompactification of Completely Regular Frames based on their Cozero Part
جبر
alg
مقاله مستقل
Original Manuscript
<p style="margin-right: 28.55pt;"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> فرض کنیم</span></span><span dir="LTR" style="position:relative;top:2.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> قاب باشد. مجموعۀ همۀ ایدهآلهای منظم از قسمت متممصفر</span></span><span dir="LTR" style="position:relative;top:2.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">؛ یعنی</span></span><span dir="LTR" style="position:relative;top:3.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">، را با </span></span><span dir="LTR" style="position:relative;top:7.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> نشان میدهیم. در این مقاله به بررسی این ایدهآلها میپردازیم. نشان میدهیم که</span></span><span dir="LTR" style="position:relative;top:7.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> قابی کاملاً منظم و فشرده است و نگاشت </span></span><strong><span dir="LTR" style="position:relative;top:7.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span></strong><strong><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span></strong><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> با ضابطۀ</span></span><span dir="LTR" style="position:relative;top:6.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> فشردهسازی برای</span></span><span dir="LTR" style="position:relative;top:2.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span> <span style="font-family:b nazanin;"><span style="font-size:10.0pt;">است که با فشردهسازی استون- چک؛ یعنی</span></span><span dir="LTR" style="position:relative;top:5.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">، یکریخت است. همچنین نشان داده شده است</span></span> <span style="font-family:b nazanin;"><span style="font-size:10.0pt;">که</span></span><span dir="LTR" style="position:relative;top:6.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">دارای الحاقی راست</span></span><span dir="LTR" style="position:relative;top:7.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> با ضابطۀ</span></span><span dir="LTR" style="position:relative;top:7.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> است. علاوه بر این، عناصر اول و فشرده قاب </span></span><span dir="LTR" style="position:relative;top:7.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> را مشخص کرده و ارتباط بین ایدهآلهای منظم</span></span><span dir="LTR" style="position:relative;top:3.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> و</span></span><span dir="LTR" style="position:relative;top:2.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">-قابها را بررسی میکنیم. افزون بر اینها نشان داده شده است که قاب</span></span><span dir="LTR" style="position:relative;top:2.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="position:relative;top:2.0pt;"><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">،</span></span></span><span dir="LTR" style="position:relative;top:2.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">-قاب است اگر و تنها اگر هر ایدهآل</span></span><span dir="LTR" style="position:relative;top:3.0pt;"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"> </span></span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;"></span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> منظم باشد.</span></span><br>
<strong><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">ردهبندی ریاضی(2010): </span></span></strong><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">22</span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">D</span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">06، 55</span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">F</span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">03، 25</span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">D</span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">18، 30</span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">D</span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;">54.</span></span></p>
<p> Let L be a frame. We denoted the set of all regular ideals of cozL by rId(cozL) . The aim of this paper is to study these ideals. For a frame L , we show that rId(cozL) is a compact completely regular frame and the map j<sub>c</sub> : rId(cozL)→L given by j<sub>c</sub> (I)=⋁I is a compactification of L which is isomorphism to its Stone–Čech compactification and is proved that j<sub>c</sub> have a right adjoint r<sub>c</sub> : L → rId(cozL) , given by r<sub>c</sub>(a)={x∈cozL : x≺≺a}. Moreover we identify prime and compact elements of rId(cozL) and we investigate the relation between regular ideals of cozL and P-frames. In addition it is shown that a frame L is a P-frame if and only if any ideal of cozL is regular.<a href="./files/site1/files/51/%D8%B9%D8%A7%D8%A8%D8%AF%DB%8C.pdf">./files/site1/files/51/%D8%B9%D8%A7%D8%A8%D8%AF%DB%8C.pdf</a></p>
فشردهسازی, قاب کاملاً منظم , ایدهآل منظم, قسمت متممصفر قاب, فشردهسازی استون- چک.
Compactification, Completely regular frame, Regular ideal, Cozero part of a frame, Stone–Čech compactification
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http://mmr.khu.ac.ir/browse.php?a_code=A-10-162-1&slc_lang=fa&sid=1
Mostafa
Abedi
مصطفی
عابدی
abedi@esfarayen.ac.ir
10031947532846002676
10031947532846002676
Yes
Esfarayen University of Technology
مجتمع آموزش عالی فنی مهندسی اسفراین، گروه ریاضی
Ali Akbar
Estaji
علی اکبر
استاجی
aaestaji@hsu.ac.ir
10031947532846002677
10031947532846002677
No
Hakim Sabzevari University
دانشگاه حکیم سبزوازی، گروه ریاضی