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 ‎...

Fuzzy linear regression (FLR) model can be thought of as a fuzzy variation of classical linear regression model. It has been widely studied and applied in diverse fields. When noise exists in data, it is a very meaningful topic to reveal the dependency between the parameter h (i.e. the threshold value used to measure degree of fit) in FLR model and the input noise. In this paper, the FLR model ...

Veech groups uniformize Teichmüller geodesics in Riemann moduli space. We gave examples of infinitely generated Veech groups; see Duke Math. J. 123 (2004), 49–69. Here we show that the associated Teichmüller geodesics can even have both infinitely many cusps and infinitely many infinite ends.

In this note we exhibit a condition under which a sequence of elements a19 , an in a commutative noetherian local ring A form an Asequence, and derive a number of corollaries. Recall that if M is an A-module, then a19 , an is an M-sequence if 1) ai+1 is a nonzerodivisor on M/(a19 9a1)M for i = 0, 9n — 1,. and 2) M Φ (al9 . . . , α n ) M . If a19 , an is an A-sequence and / is the ideal generate...

microorganisms play a major role in the initiation and perpetuation of pulpal and periapical disease. in order to predictably achieve a bacteria-free root canal system, it is necessary to use intracanal medicaments. calcium hydroxide is the most common intracanal medicaments. it is effective against primary infections. however, its effectiveness against enterococcus faecalis and candida albican...

Let R be a regular ring, let J an ideal generated by sequence of codimension at least 2, and I containing J. We give example module HI3(J) with infinitely many associated primes, answering question Hochster Núñez-Betancourt in the negative. In fact, for i≤4, we show that under suitable hypotheses on R/J, AssHIi(J) is finite if only AssHIi−1(R/J) finite. Our proof this statement involves novel g...

A concept of ideal extensions in ternary semigroups is introduced and throughly investigated. The connection between an ideal extensions and semilattice congruences in ternary semigroups is considered.

In this paper we shall apply modules of generalized fractions to extend the notion of the grade of an ideal, and to obtain characterizations of Gorenstein rings.

Let S be a set of n ideals of a commutative ring A and let Geven (respectively Godd) denote the product of all the sums of even (respectively odd) number of ideals of S. If n ≤ 6 the product of Geven and the intersection of all ideals of S is included in Godd. In the case A is an Noetherian integral domain, this inclusion is replaced by equality if and only if A is a Dedekind domain.