An old question of T. Jech and K. Prikry asks if an existence of a precipitous ideal implies necessary existence of a normal precipitous ideal. The aim of the paper is to prove some results in the positive direction. Thus, it is shown that under some mild assumptions, an existence of a precipitous ideal over א1 implies an existence of a normal precipitous ideal over א1 once a Cohen subset is ad...

let $r$ be a commutative ring with identity‎. ‎a proper ideal $p$ of $r$ is a $(n-1,n)$-$phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin r$‎, ‎$a_1cdots a_nin pbackslash p^m$ ($a_1cdots a_nin pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin p$‎, ‎for some $iin{1,ldots,n}$; ($m,ngeq 2$)‎. ‎in this paper several results concerning $(n-1,n)$-$phi_m$-prime and $(n-1,n)$-...

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 ‎...

Table of contents 1. Primary ideals 1 2. Primary modules 3 3. Primary decompositions 6 4. More ways to get associated primes 11 5. Witnesses 14 6. Canonical primary decomposition 17 7. Associated primes of powers of an ideal 18 8. Primary decompositions of powers of an ideal 20 9. An algorithm for computing primary decompositions 24 10. Complexity of associated primes 28 11. Exercises 31 Biblio...

RESULTS ON N-ABSORBING IDEALS OF COMMUTATIVE RINGS by Alison Elaine Becker The University of Wisconsin-Milwaukee, 2015 Under the Supervision of Dr. Allen Bell Let R be a commutative ring with 1 6= 0. In his paper On 2-absorbing ideals of commutative rings, Ayman Badawi introduces a generalization of prime ideals called 2-absorbing ideals, and this idea is further generalized in a paper by Ander...

1. Primary ideals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Primary modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. Primary decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 4. More ways to get associated primes . . . . . . . . . . . . . . . . . . . . . . . 12 5. Witnesses . . . . . . . . . . . . . . . . . . ...

Interprofessional education is a core competency for nursing, medicine, pharmacy, dentistry, and public health (Interprofessional Education Collaborative Expert Panel, 2011). This article describes an innovative experiential exercise for postlicensure learners—adult and family nurse practitioner students and medical resident physicians. The aim of this interdisciplinary activity was to trial an...

Inductive Logic Programming (ILP) algorithms are frequently used to data mine multi-relational databases. However, in many ILP algorithms the use of primary key constraints is limited. We show how primary key constraints can be incorporated in a downward refinement operator. This refinement operator is proved to be finite, complete, proper and therefore ideal for clausal languages defined by pr...