fa بُعدهای انژکتیو گورنشتاین و کوهن-مکالی بودن جبر alg مقاله مستقل Original Manuscript <span style="font-family:b nazanin;"><span style="font-size:10.0pt;">فرض کنیم </span></span><span dir="LTR"><span style="font-family:times new roman,serif;"><span style="font-size:10.0pt;">(<em>R</em>,m)</span></span></span><span style="font-family:b nazanin;"><span style="font-size:10.0pt;"> حلقه‌ای موضعی،</span></span> <span style="font-family:b nazanin;"><span style="font-size:10.0pt;">نوتری و جابه‌جایی باشد.</span></span> <span style="font-family:b nazanin;"><span style="font-size:10.0pt;">در این مقاله وجود مدول‌های متناهی مولد از بُعد انژکتیو گورنشتاین متناهی روی حلقه‌های کوهن-مکالی را بررسی می‌کنیم. در ابتدا بُعدهای انژکتیو گورنشتاین کوهمولوژی موضعی هم‌بافت‌ها را بررسی می‌کنیم</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;"></span></span><br> &nbsp; Throughout this paper&lrm;, (<em>R</em>, m) is a&lrm; commutative Noetherian local ring with the maximal ideal <strong>m</strong>. &lrm;The following conjecture proposed by Bass [1]&lrm;, &lrm;has been&lrm; proved by Peskin and Szpiro [2] for almost all rings: &lrm;<br> <strong>(B)</strong> <em>If R admits a finitely generated R-module of&lrm; finite injective dimension&lrm;, &lrm;then R is Cohen-Macaulay</em>.<br> &lrm;The problems treated in this paper are closely related to the&lrm; following generalization of&nbsp; Bass conjecture which is still wide&lrm; open:&lrm;<br> <strong>(GB)</strong> <em>If R admits a finitely generated R-module of&lrm; finite Gorenstein-injective dimension&lrm;, &lrm;then R is&lrm; Cohen-Macaulay</em>.<br> &lrm;&nbsp; Our idea goes back to the first steps of the solution of Bass conjecture given by Levin and Vasconcelos in 1968 [3] when <em>R</em> admits a&lrm; finitely generated<em> R</em>-module of injective dimension <img alt="" height="19" src="file:///C:/Users/1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.gif" width="11" >1&lrm;.<br> Levin and Vasconcelos indicate that if&lrm; <img alt="" height="19" src="file:///C:/Users/1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.gif" width="67" >is a non-zerodivisor&lrm;, &lrm;then for&lrm; every finitely generated <em>R/xR</em>-module<em> M</em>&lrm;, &lrm;there is&lrm; <img alt="" height="21" src="file:///C:/Users/1/AppData/Local/Temp/msohtmlclip1/01/clip_image006.gif" width="130" >&lrm;. &lrm;Using this fact&lrm;, &lrm;they construct a&lrm; finitely generated <em>R</em>-module of finite injective dimension in&lrm; the case where <em>R</em> is Cohen-Macaulay (the converse of Conjecture&lrm; <strong>B</strong>)&lrm;. <span dir="RTL"></span><br> &lrm; In this paper we study the Gorenstein injective dimension of local cohomology&lrm;. &lrm;We also show that if <em>R</em> is Cohen-Macaulay&lrm; with minimal multiplicity&lrm;, &lrm;then every finitely generated module&lrm; of finite Gorenstein injective dimension has finite injective&lrm; dimension.&lrm;<br> &lrm;We prove that a Cohen-Macaulay local ring&lrm; has a finitely generated module of&lrm; finite Gorenstein injective dimension.&lrm;<br> <a href="./files/site1/files/52/4.pdf">./files/site1/files/52/4.pdf</a> انژکتیو گورنشتاین, حلقه‌‌های کوهن-مکالی, مدول‌های کوهمولوژی موضعی Gorenstein injective, Cohen-Macaulay ring and Local cohomology modules 157 164 http://mmr.khu.ac.ir/browse.php?a_code=A-10-392-1&slc_lang=fa&sid=1 Reza Sazeedeh رضا سزیده rsazeedeh@ipm.ir 10031947532846003061 10031947532846003061 Yes Urmia University دانشگاه ارومیه، دانشکدۀ علوم، گروه ریاضی fatemeh Savoji فاطمه ساوجی f.savoji@urmia.ac.ir 10031947532846003062 10031947532846003062 No Urmia University دانشگاه ارومیه، دانشکدۀ علوم، گروه ریاضی