Let Io and m° be the ideals associated with Laver and Miller forcing, respectively. We show that add(/°) < cov(/°) and add(m°) < cov(m°) are consistent. We also show that both Laver and Miller forcing collapse the continuum to a cardinal < f). Introduction and notation In this paper we investigate the ideals connected with the classical tree forcings introduced by Laver [La] and Miller [Mi]. La...

Let $R$ be a commutative ring with identity and $mathbb{A}(R)$ be the set   of ideals of $R$ with non-zero annihilators. In this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $R$, denoted by $mathbb{AG}_P(R)$. It is a (undirected) graph with vertices $mathbb{A}_P(R)=mathbb{A}(R)cap mathbb{P}(R)setminus {(0)}$, where   $mathbb{P}(R)$ is...

The ovigerous females of Upogebia (Upogebia assisi) were collected from Pacha (24o 50 54&quot;N, 66o 43 E) on October 6 and 7, 1994 and 1995 respectively. They were kept for rearing under laboratory conditions at room temperature (25-32oC) in the filtered seawater with salanity of 35-36 parts per thousand (ppt) and pH 7.8-9. Development of larvae proceeds from first to three or four zoeal and p...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ‎ring of continuous real-valued functions on $l$‎. ‎we show that the‎ ‎lattice $zid(mathcal{r}l)$ of $z$-ideals of $mathcal{r}l$ is a‎ ‎normal coherent yosida frame‎, ‎which extends the corresponding $c(x)$‎ ‎result of mart'{i}nez and zenk‎. ‎this we do by exhibiting‎ ‎$zid(mathcal{r}l)$ as a quotient of $rad(mathcal{r}l)$‎, ‎the‎ ‎...

background & aim: considering the lack of information regarding the effects of religion on young couples’ fertility preferences, this study aimed to evaluate the relationship between religious beliefs and fertility preferences among engaged couples in mashhad, iran, in 2013. methods:this cross-sectional study was conducted on 450 engaged couples, referring to premarital counseling clinics at he...

In this paper, using N-structure, the notion of an N-ideal in a BE-algebra is introduced. To obtain a more general form of an N-ideal, a point N-structure which is (k-conditionally) employed in an N-structure is proposed. Using these notions, the concept of an ([e], [e]∨ [ck])-ideal is introduced and related properties are investigated. The notion ([e], [e]∨ [ck])-ideal is a generalization of (...