‎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 ...

‎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 ...

In this paper, we introduce the concept of canonical stretched rings, sparse rings and maximum ideals. Then give characterizations rings; a characterization Gorenstein in terms their Several explicit examples are provided along paper to illustrate such rings.

purpose: to report a known case of leprosy with bilateral corneal scars. case report: we present a 70 year-old man who had developed claw hand deformity and loss of sensation in the extremities secondary to leprosy since 7 years ago. two years ago, he presented with loss of vision due to lagopthalmos and loss of corneal sensation for which he had undergone lateral tarsorrhaphy at the time. conc...

background: uterine rupture at the site of a previous cesarean scar is an uncommon but catastrophic complication of pregnancy, which is associated with significant maternal and fetal morbidity and mortality. case presentation: a 30-year old woman at 24th week of gestation and complaint of pain, contractions and spotting was admitted in royan institute in tehran, iran. she had a past medical his...