توجه: محتویات این صفحه به صورت خودکار پردازش شده و مقاله‌های نویسندگانی با تشابه اسمی، همگی در بخش یکسان نمایش داده می‌شوند.
۱A class of Artinian local rings of homogeneous type
نویسنده(ها):
اطلاعات انتشار: Bulletin of Iranian Mathematical Society، چهلم،شماره۱(پياپي ۸۷)، ۲۰۱۴، سال
تعداد صفحات: ۲۵
Let $I$ be an ideal in a regular local ring $(R,n)$ , we will find bounds on the first and the last Betti numbers of $(A,m)=(R\I,n\I)$ . if $A$ is an Artinian ring of the embedding codimension $h$ , $I$ has the initial degree $t$ and $mu(m^t)=1$ , we call $A$ a {it $t–$extended stretched local ring} . This class of local rings is a natural generalization of the class of stretched local rings studied by Sally , Elias and Valla . For a $t–$extended stretched local ring , we show that ${h+t–2choose t–1}–h+1leq tau(A)leq {h+t–2choose t–1}$ and $ {h+t–1choose t}–1 leq mu(I) leq {h+t–1choose t}$ . Moreover $tau(A)$ reaches the upper bound if and only if $mu(I)$ is the maximum value . Using these results , we show when $beta_i(A)=beta_i(gr_m(A))$ for each $igeq 0$ . Beside , we will investigate the rigid behavior of the Betti numbers of $A$ in the case that $I$ has initial degree $t$ and $mu(m^t)=2$ . This class is a natural generalization of {it almost stretched local rings} again studied by Elias and Valla . Our research extends several results of two papers by Rossi , Elias and Valla .
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